Talk:Cosmic inflation/Archive 1

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Has anyone come across a resolution concerning temporal consequences of cosmic inflation making the universe expand faster than the speed of light? i.e., if the universe's outer boundary is moving that fast, then it can travel backward in time, causing an implosion, a duplication of all matter, and massive temperature/density increase until the inflationary period ended.

Which might not be a bad thing, as it would increase information transfer between the universe's parts, but has this been addressed at all?

Apparently there is no temporal consequence from SR, since relativistic time reversal only applies to things moving through space but not the expansion of space itself.

The speed of light can be defined only in terms of the metric tensor; inflation theory uses a metric with nonzero curvature; making that argument invalid.

63.205.40.227 02:05, 4 Feb 2004 (UTC)

The metric tensor is well defined in inflation, and nothing can move through space faster than the speed of light. But here space itself os the thing that moves, causing the distance which seperates two stationary points to grow bigger and bigger, so that one point would be seen from the other point as if it moves faster than the speed of light. Shokopuma 19:54, 26 April 2006 (UTC)

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I think this overstates the case. WMAP supports cosmic inflation but it is one of several supporting bits of evidence.

This theory was revealed to be correct with NASA's historic February 11, 2003 release of data collected from the Wilkinson Microwave Anisotropy Probe (WMAP).

---

I have a question. If it's true that the Universe is expanding in a accelerated rate, then would cosmic inflation explain universe's current accelerated expansion rate?

No. Inflation refers to a very brief period in the early universe when the rate of expansion of the universe increased dramatically. As soon as inflation ended, the universe continued expanding at a more conservative rate. However, if everything in the universe attracts everything else gravitationally then we would expect the expansion to slow down over time through this mutual attraction between all objects. The 'fact' (still some controversy over this) that the expansion is not slowing down but rather accelerating means that despite gravity trying to hold everything together, there is another force at work driving this 'anti-gravity' effect and increasing the expansion rate. This new force is generally referred to as dark energy (not to be confused with dark matter) and is thought to make up about 70% of the critical density required to close the universe.

However, some people think that dark energy doesn't exist at all, and that the solution is to modify general relativity to modify the action of gravity over cosmological distance scales. DH79 11:53, 14 October 2006 (UTC)

If GR would be revised, then the whole picture of the expanding universe might be thrown out of the window as well, at least when some other viable concept comes up to explain the CMBR and the redshift-distance corelation. Heusdens 14:04, 10 January 2007 (UTC)

Actually that's not quite the complete picture -- the current "accelerating" expansion of the universe is a lot like inflation in that both may be modelled by a constant Hubble factor. In the modern picture the universe expanded very rapidly with a constant Hubble factor during the inflationary phase: then the expansion slowed with the decrease of the Hubble factor: now the decline in the Hubble factor is/has tailed off and the expansion has stablised again -- albeit at a much lower level than previously. --Michael C. Price ^talk 21:51, 14 October 2006 (UTC)

Thanks for that extra info Michael. Just one further point - am I right in thinking that the mechanism that drove inflation (scalar field in a potential well) is not thought to be the same reason that we now have an acceleration of the expansion rate (energy density of the vacuum due to Planck scale quantum fluctuations)? These may be two ways of expressing the same physics, but if so I'm unaware of it. DH79 17:02, 15 October 2006 (UTC)

Yes, the mechanisms are different, but that's probably all we can say with certainty. The current accelerated expansion may be due to a cosmological constant (a constant term in the Einstein field equations) and early universe inflation may be due a scalar field (the Higgs?), but no one knows for sure about either -- yet. --Michael C. Price ^talk 17:51, 15 October 2006 (UTC)

negative pressure vacuum energy density

What is vacuum energy density? Do you mean false vacuum? How could vacuum itself (with no mass-energy) contain pressure? Do you mean that spacetime has an energy which is always positive (or non-zero)? Is it because according to Einstein's theory of general relativity, bodies create the space around them? -- Orionix 22:30, 9 Mar 2005 (UTC)

Vacuum energy is not really related to the false vacuum -- a true vacuum can have an energy density as well. One thing that quantum field theory has taught us is that there is energy in a vacuum -- see Casimir effect. With energy comes pressure, since pressure is just the work done to change the volume of a box. In the case of vacuum energy, the pressure is negative since increasing the volume of the box increases the energy, and so you must do work on the box (with an ordinary gas of particles, it is the opposite). Gravity, however, is strange, and making spacetime have positive energy actually makes the expansion accelerate. See the explanation under cosmological constant in dark energy. --Joke137 17:02, 10 Mar 2005 (UTC)

Hi, thanks for the explanation.

I'm really not an expert in the mathematics of QFT but i know the basic idea which is that at high energies matter is better described by fields rather than by classical means.

This great work may also teach us one day that discrete particles do not exist and that all matter is a wave structure, continuous in the space it occupies (or is part of).

I was wondering whether cosmic inflation could explain how the universe came into being and also why it's accelerating. According to what i understood, cosmic inflation occurred during the time of superunification (Planck era, $10^{43}$ second) or grand unification (GUT era, $10^{35}$ second) while the universe existed in a state of nonzero energy density (also called false vacuum). A false vacuum is a combination of mass density and negative pressure that results gravitationally in a large repulsive force (antigravity).

A problem with this theory is the "graceful exit" (the fine-tuning). As of 2005, do you have any idea of how this problem could be solved in inflation? -- Orionix 18:30, 14 Mar 2005 (UTC)

In answer to some of your questions... Inflation does not provide any explanation of what happened before inflation. In fact, some theorists think that generating the necessary initial conditions for inflation to start is a major problem for inflation. There was indeed a much larger energy density during the early universe inflation than the energy density which we observe in the universe today, but this is not necessarily a false vacuum. The original idea by Guth did use a false vacuum and this lead to the so called graceful exit problem. However, that was abandoned in favor of other models which do not suffer from this problem. There is still a fine tuning problem with any known inflation models, where fine tuning has a technical meaning, but this is not the graceful exit problem of the old inflation based on a false vacuum. -- matt 19 Mar 2005

Removing link

Removing link 13 things do... The Link dose not link to anything related to the article. Johan Bressendorff

Gravitational energy density

A problematic quote has been inserted a couple of times:

A generic property of inflation is the balancing of the negative energy of the gravitational field, within the inflating region, with the positive energy of the inflaton field to yield a post-inflationary universe with negligible or zero energy density. Alan Guth says "Since the negative energy of a gravitational field is crucial to the notion of a zero-energy universe, it is a subject worth examining carefully. In this appendix I will explain how the properties of gravity can be used to show that the energy of a gravitational field is unambiguously negative." (See Guth's "The Inflationary Universe" (ISBN 0224044486) Appendix A) It is this balancing of the total universal energy budget that enables the open-ended growth possible with cosmic inflation; during inflation energy flows from the gravitational field (or geometry) to the inflaton field -- the total gravitational energy decreases (becomes more negative) and the total inflaton energy increases (becomes more positive). But the respective energy densities remain constant and opposite since the region is inflating. Consequently inflation explains the otherwise curious cancellation of matter and gravitational energy on cosmic scales which is a feature of a zero-energy universe, which is consistent with astronomical observations.

There is no such thing as the energy of the gravitational field in general relativity. This is a big problem, and people have come up with various constructions that allow energy to be measured in some circumstances, like the ADM energy. But in general it is problematic, and while I don't know the context of the quote, I think Guth is here giving a hand-waving description of how inflation functions. But I really don't know if the quote is appropriate, so I reverted the edits. At the very least, more context is needed. –Joke 15:23, 14 February 2006 (UTC)

It is not true that there is no such thing as the energy of the gravitational field in GR. To maintain conservation of energy the gravitational field must be assigned an non-tensoorial energy (generally negative) although such an energy density is not tensorial neither is it absent. Such dismissal is simplistic. The context of the quote by Alan Guth is clear from the content of the quote and title of the book, namely free-lunch aspect of inflation, a central concept and one which Guth (and others) frequently mention in both technical and popular expositions of inflation. The removal of the text is therefore unjustified on the stated grouds. However, providing more context is never a bad idea. -- MCP—The preceding unsigned comment was added by 82.2.22.65 (talk • contribs) .

I disagree. Conservation of energy is simply the statement that the stress-energy tensor is covariantly conserved, which has nothing to do with general relativity or the Einstein field equations. And I've not sure what you mean by "non-tensorial energy". Perhaps you mean that in an asymptotically flat spacetime it is possible to write the Einstein equations in such a way that they look like a wave equation plus a contribution from a Lorentz invariant, non-tensorial quantity that looks an awful lot like the stress-energy tensor of the gravitational field. This gives you the ADM energy I alluded to above. I'm not sure if it is possible to do the same in a FRW spacetime or an asymptotically de Sitter spacetime, but it is certainly not possible to do it in general, since there is no general notion of energy in general relativity. –Joke 19:22, 14 February 2006 (UTC)

Guth evidently disagrees. His quote continues: "......the energy of a gravitational field is unambiguously negative. The argument will be described [in the appendix] in the context of Newton's theory of gravity, although the same conclusion can be reached using Einstein's theory of general relativity." Nor is the sci.physics FAQ as certain that energy conservation is meaningless in GR, rather it says (and I paraphrase) that it depends on what you mean by energy and how you define it. By non-tensorial I mean that any resultant energy density and time-conserved integral is frame dependent, although the integral is conserved with time in a particular frame; however this should not disturb us (although it evidently does disturb a lot of people) since many useful quantities in physics are frame-dependent. All that is needed in the inflation article is a rider to the effect that energy conservation in GR is controversial, but that if we accept it then gravitational energy is "unambiguously negative" etc etc. -- MCP—The preceding unsigned comment was added by 82.2.29.195 (talk • contribs) .

The sci.physics FAQ says, regarding gravitational energy, "for these reasons, most physicists who work in general relativity do not believe the pseudo-tensors give a good local definition of energy density, although their integrals are sometimes useful as a measure of total energy." The pseudo-tensor, by the way, is one defined by Landau and Lifshitz in 1947. The fact is that there is no generally covariant definition of energy in general relativity. Not having general covariance is much worse than frame dependence: it doesn't merely depend on what foliation of spacelike hypersurfaces you're using to measure energy, it depends on the coordinates you're using, too! In limited situations, such as asymptotically flat spacetimes, it is possible to evade these restrictions, but in general it is not.

No, the ordinary divergence of the Landau-Lifshitz gravitational + matter pseudotensor vanishes in all frames; the divergence of the pseudo-tensor is itself a tensor. Therefore the gravitational energy/momenta are defined in all frames; its 4-flow across any closed hypersurface is identically zero.--Michael C Price 15:14, 6 May 2006 (UTC)

Therefore, it is dishonest to talk about gravitational energy.

No, see above point.--Michael C Price 15:14, 6 May 2006 (UTC)

In the context of inflation, it could be true (I don't know) that one can define energy in asymptotically FRW or de Sitter spacetimes. I wish I knew what Guth meant by "unambigiously negative" – perhaps the pseudo-tensor obeys some energy condition.

Yes, the condition obeyed is, I'm sure familar to you:

$8\pi G\rho +\gamma +-3H^{2}=0$

where rho is the inflaton energy density and other terms are defined below. For simplicity flatness assumed; extra term otherwise. The gravitational energy density is in the Hubble term: $-3H^{2}$ — -- MCP

The preceding unsigned comment was added by 82.14.0.213 (talk • contribs) .

Appendix A of his book only talks about Newtonian gravity, where it is easy enough to define energy. It seems that in his writings he refers to a 1932 paper of Tolman [1] but not to any of the various attempts to define energy in general relativity. Because of the problematic nature of these efforts, I think they are best left out of the article. –Joke 21:59, 14 February 2006 (UTC)

Guth is referring to the fact that a physical gravitating source (that is something with a non-zero stress tensor) will positively curve space (which is another way of saying that the gravitational energy in unambiguously negative if the far-field limit is defined as a background zeroed in the normal way). --ScienceApologist 23:18, 14 February 2006 (UTC)

That's true, but it's hard for me to see what it has to do with inflation. What is the gravitational energy density of the de Sitter universe? –Joke 23:24, 14 February 2006 (UTC)

Any gravitational part of the inflaton field (apart from that which can be shoved into a scalar field) will have a negative gravitational energy density. --ScienceApologist 23:32, 14 February 2006 (UTC)

What do you mean by gravitational part of the inflaton field? In most of the models I've seen, the whole thing is a scalar field. Even in the curvaton model, it's just a scalar field coupling to the Einstein-Hilbert term. –Joke 17:27, 15 February 2006 (UTC)

Inflation has an entire set of models that can be applied with as many moments of the field you want including linear, quadratic, etc. Any "generic" inflation model includes contributions that both gravitate and contributions that inflate. If you consider the inflaton field to be simply the scalar part then that's that, but if you are interested in characterizing the actually dynamics of inflation then the "inflaton field" is everything in the universe including potentially pesky stuff that isn't a part of the scalar field. That's how I remember modeling inflationary scenarios, anyway. --ScienceApologist 19:46, 15 February 2006 (UTC)

I must say, I don't really understand what you are referring to here. The inflaton is just a scalar field in the vast majority of models. The potential energy of that scalar field causes the universe to expand exponentially. The flatness of the potential energy, as a function of the field, causes it to continue to do so for an extended period. The contributions that "gravitate" you are referring to are perhaps the perturbations of the homogeneous scalar field? (Actually, because of gauge invariance, there is a degeneracy between fluctuations of the Newtonian potential and fluctuations of the scalar field, and one is usually eliminated, often the scalar field – is this what you're talking about?) –Joke 23:25, 15 February 2006 (UTC)

Yes, I agree. It is not dishonest to talk about gravitational energy. In a de Sitter universe (which is all we are concerned about here) the gravitational energy density is:

$-3H^{2}/8\pi G$

$G$ = Newton's constant

$H$ = Hubble's expansion factor

Note the negative sign! —The preceding unsigned comment was added by 82.14.0.213 (talk • contribs) .

You could apply the same reasoning to any FRW universe to get the energy density.

Which is no doubt how Landau and Lifshitz were able to show that in any closed universe the gravitational and matter energies cancelled exactly (Guth, ibid p273). Previously this had just been seen as a curious mathematical result; in the aftermath of inflation it takes on physical signficance in a "free-lunch" universe. -- MCP

That doesn't make it sensible! While this definition works in any FRW spacetime without spatial curvature because there is a preferred foliation in terms of flat, spacelike hypersurfaces. In that case, in appropriate coordinates, this is the Hamiltonian constraint in canonical gravity. This only works because there are preferred coordinates in FRW universes. In a more general situation, it depends on your coordinate system (i.e. it is not gauge invariant). Maybe the Laundau-Lifshitz pseudotensor obeys some general energy conditions, but the Friedman equation is not enough for the general case. Even in the de Sitter case, how would you define it if you were handed the space in the closed or static slicing? –Joke 17:27, 15 February 2006 (UTC)

We are not concerned with the more general cases; inflating universes are very symmetric, with a natural choice of preferred comoving frames. In them, as in Newtonian gravity, the gravitational field can be assigned an energy density. Moving from flat to closed (or hyperbolic) we have to add a curvature term to get the gravitational energy density (a side issue, though, since spatial curvature will rapidly vanish under inflation as spatial flatness is achieved). -- MCP

On this issue, see also the comments by User:Hillman at Talk:Cooperstock's Energy Localization Hypothesis. –Joke 23:03, 25 August 2006 (UTC)

Note Hillman's comment:

There is no doubt that in the end, general relativity does respect conservation of energy.

See also Stress-energy-momentum pseudotensor and note that conservation of energy-momentum holds quite generally:

the total energy-momentum crossing the hypersurface of any closed space-time hypervolume vanishes.

The objection to the use of pseudotensors is quite mistaken since it is the derivative of the Landau-Lifshitz pseudotensor which is used and this entity is a tensor (which vanishes everywhere even in an arbitary geometry). --Michael C. Price ^talk 05:02, 26 August 2006 (UTC)

Since there has been no substantive technical response for awhile now I shall amend the article accordingly. --Michael C. Price ^talk 23:52, 1 November 2006 (UTC)

The Landau-Lifshitz pseudotensor is used to define energy. It is coordinate dependent. Therefore, when we speak of "gravitational energy" we are not speaking of a quantity that is meaningful in any physical (coordinate independent) sense. Just because the currents are tensorial doesn't solve the problem. What changes do you propose to make? I just think that trying to add something about "gravitational energy" opens a big, unnecessary can of worms. –Joke 02:35, 2 November 2006 (UTC)

Guth and Hawking (page p129, Brief History of Time) do not agree; both explain energy conservation in terms of negative gravitational energy -- it is the whole essence of the "free lunch" quote. Sweeping the issue under the carpet is not a solution. --Michael C. Price ^talk 05:49, 2 November 2006 (UTC)

Arrow of time, second law of thermodynamics

This is a complex debate, but two things seem clear

• While gravity may not strictly break the second law of thermodynamics, it can certainly circumvent it through mechanisms like cosmic inflation which dilute entropy, sending the entropy density to (near) zero.

I agree --Michael C Price 19:09, 2 May 2006 (UTC)

• Talking about whether gravity conserves energy or not is meaningless (see above). The fact is, that the stress-energy tensor is covariantly conserved in GR, which is the analogue of classical energy conservation. You can, in some situations, define a total energy that is conserved, but this concept is clearly not meaningful in all situations, and there is no such thing as the local gravitational energy density. See the extensive discussion above.

–Joke 19:04, 28 March 2006 (UTC)

My unanswered points (yes, see previous discussion!) testify that the issue of gravitational energy conservation is not as meaningless or as simplistic as you've presented here. --Michael C Price 19:09, 2 May 2006 (UTC)

Graceful Exit Problem

I'd like a little clarification on the graceful exit problem, if anyone can provide it. Two statements of the problem: "As noted by Guth himself [53], however, collisions of the walls of very large bubbles should lead to an unacceptable destruction of homogeneity and isotropy in the universe after inflation."[2] The article he cites is [3], and says that reheating requires bubble collisions that won't occur because the bubbles of the same size get pushed apart. However, he mentions percolation as a possibility (which would involve all the bubbles clustering together and creating an infinite region of true vacuum), and I wonder if that would create unaccaptable CMB fluctuations?

So, the question... can the graceful exit problem be restated as "Bubbles of true vacuum are created in the false vacuum but remain cold because inflation pushes these regions away from each other much faster than they grow." ? Also, is bubble collision ruled out as a reheating mechanism in other models (e.g. because of the domain wall problem)? --Keflavich 20:05, 4 May 2006 (UTC)

Yes. I have tried to clarify this. There is something called new old inflation which is supposed to alleviate this problem, but it is probably not yet significant enough for inclusion in the article. –Joke 17:41, 18 May 2006 (UTC)

Expert wanted?

User 86.141.57.167 (talk · contribs) added an "expert wanted" template on the article page. I do not find any confirmation this is the case. There are two points discussed here in May but neither in recent few days. Therefore I'll revert his edit for now, at least until 86.141.57.167 explains his/her edit. If any other user feels the template should be there, please fell free to put it back. Friendly Neighbour 10:24, 17 May 2006 (UTC)

Some comments

• Someone added the assertion that Andrei Linde believes inflation can be past eternal. I do not dispute this, but is there a source?

Since it just needs a source why not leave it in and add a citation needed tag? -- that way someone is more likely to supply it. And yes, I read about Linde's views but don't have the cite immediately to hand.--Michael C Price 21:56, 15 June 2006 (UTC)

• • Here is a source: Andrei Linde, "Inflation and String Cosmology," eConf C040802 (2004) L024; J.Phys.Conf.Ser. 24 (2005) 151-160 (available from arXiv:hep-th/0503195 v1 24 Mar 2005). Not sure if it has actually been peer reviewed, but it was presented at different technical symposia, and Dr. Linde does discuss in this paper his opinion that even though any particular past-directed geodesic must have finite length, there is no reason to conclude that there must be an upper limit on that length, so inflation can be eternal in the past. 138.162.5.12 17:33, 25 July 2006 (UTC)Robert Preisser
    • Thanks. Have added it to article. --Michael C. Price ^talk 01:11, 7 August 2006 (UTC)

• The description of hybrid inflation was incorrect. It is eternal, just like new inflation. In fact, it is not clear that it is possible to construct a model of inflation that is not eternal.
• Inflation should not be thought of as a rapid cooling. It has a de Sitter temperature on the order of 10¹⁶ GeV.

–Joke 21:45, 15 June 2006 (UTC)

Not necessarily. Read page 13 of this: http://arxiv.org/abs/hep-th/0402051 . It says that most models of hybrid inflation are not eternal.

FYI: Someone signing as ScienceApologist can not be located by user talk and has sent me a message. User:Malangthon

Merge

I have suggested that inflationary cosmology be merged into this article, since they seem to be essentially the same thing. Salmar 02:25, 7 August 2006 (UTC)

Yes, that is a no brainer. I was bold and did it. –Joke 16:00, 9 August 2006 (UTC)

Kinematic inflation

New section by an obssesive "Milne Cosmology" pusher , as far as I can see. Nothing to do with inflation. --Michael C. Price ^talk 17:44, 9 August 2006 (UTC)

Milne Cosmology pusher? Do you know, until a month ago, I had been arguing this cosmology for five years and nobody ever identified me as a Milne Cosmology pusher. Well, since nobody else seems to be pushing it, and to my knowledge, nobody has ever given reason to discount Milne's Cosmology, I have to do it myself. What exactly is it that you wish inflation to do if not to move the boundaries of the universe to a position further than would be allowable by the speed of light? This has everything to do with inflation. --Jonathan Doolin

Your insert contained factual errors and irrelevancies. For instance you state (without sources):

Part of the difficulty of describing inflation in the Standard cosmological model is that the standard model aspires to describe the shape of the universe from ALL reference frames at the same time.

This is just plain incorrect. Ever heard of the co-moving frame of reference?

Consider the balloon model that Eddington originally made popular. In this, he represents all particles of the universe "in" the surface of a balloon, thus obtaining a homogeneous distribution of matter with no center. By doing so, he is attempting to treat all of the particles of the universe from the viewpoint of an omniscient observer who sees all of the particles at once at some meta-instant of time. This, I would call aspiring to describe the shape of the universe from all references frames at the same time.

Also, Milne describes how homogeneity can be achieved by taking each observer associated with a particular event where the observer is at a specified density. By defining a coordinate system based on these events, you have constructed a geometry where the universe is homogeneous. However, this also describes the universe from all reference frames at the same time (unless some reference frames are not occupied by any observers.)

Unfortunately, you'll probably not find a book based on the standard model which is quite so clear on what the standard cosmological model is aspiring to do. These models generally begin by assuming universal homogeneity, and they must either mean homogeneity in terms of a single Euclidian space, or homogeneity in some Riemannian geometry.

If the model assumes homogeneity in Euclidian space, then universal homogeneity can only be accomplished in a static universe, thus all observers are comoving, and Hubble's Law does not apply, (redshifts would have to be caused by some other effect besides recession velocity.) I would regard this as highly unlikely.

If the model assumes homogeneity in any other Riemannian geometry, it is an attempt to treat all reference frames at the same time. Milne calls this a "mixed" coordinate system, where coordinates are established by observers who are at different locations and traveling at different speeds.

Your efforts would be better rewarded if you created a Milne Model article and explained there why it is so wonderful (as indeed it may be). --Michael C. Price ^talk 20:55, 9 August 2006 (UTC)

As time permits, I will. Thank you. If you know any other obsessive Milne Pushers, please let me know. I am not in the loop and would very much like to be.

Your explanation seems very confused at multiple levels. However it is not my job to explain general relativity. I note, though, that Milne didn't accept GR, whereas all models of inflation work within this paradigm. Application of Milne to inflation is therefore original research and expressly forbidden in Wikipedia. Good luck writing your article on the subject (and I'm not being sarcastic), but don't think it has any relevance here. --Michael C. Price ^talk 17:37, 10 August 2006 (UTC)

Penrose Criticism and the entropy "problem"

Can someone explain the statement:

In [Penrose]'s opinion the biggest mystery of the Big Bang is why the universe started in a state of very low entropy. Rather than solving this problem, the inflation theory further aggravates it--the thermalization at the beginning of the inflation era pushes the initial entropy even lower--essentially requring the universe to start in a more ordered state.

Surely inflation reduces any "entropy problem"? If we require consistency with observations then the pre-inflationary region of the universe required to be in a low-entropy state is much smaller than the size of the initial low-entropy region required in a non-inflationary theory. --Michael C. Price ^talk 00:07, 4 September 2006 (UTC)

Penrose seems to have problems not only with Cosmic inflation but also string theories and quantum mechanics in general (see this article). He seems to be a mathematician who by working for one field of physics (cosmology) became known as a "mathematical physicist", whatever that means. I belive his physics intuition is not much higher than the average for matematicians (that is pretty low). In general, I've seen many old scientists disbelieving any new theory they hear about.

Now, more to the point. The criticim Penrose narrates in his book is not originally his own. It comes from a paper D.N. Page, 1983, "Inflation doesn not explain time asymmetry" Nature, 304, 39 (actually a reply to an article by P.C.W. Davies, 1983, "Inflation and time asymmetry in the Universe", Nature, 301, 398). The reply to the criticism (P.C.W. Davies, 1984, "Inflation to the universe and time asymmetry", Nature, 312, 524) is actually accepting the premise that the initial state of the visible Universe (originally a microscopic amount of space before the inflation) had to have a very low entropy due to random quantum fluctuations to account for the observed thermodynamic arrow of time. However this is not a problem but a bonus for the inflation theory. The fact that the small fragment of space from which our Universe grew had to be extremely orderly to allow inflation can makes it unnecessary to make any ad-hoc theories about the initial entropy state which are necessary in other theories.

The fact that Penrose still clings to the argument (in my opinion successfully refuted) of Page after 20 years, does not make him a cutting edge criticist of the Cosmic inflation. I believe the article section should be reworked giving their due to Page and Davis for proposing this line of critique and for refuting it. Friendly Neighbour 06:34, 4 September 2006 (UTC)

Perhaps we should create an entropy problem article, along the lines of the flatness problem and monopole problem? The Penrose's objection can be demolished there.--Michael C. Price ^talk 09:07, 4 September 2006 (UTC)

I reworked the section, adding the original author of the critique and its rebuttal. Also, I removed the fractal sentences. Who else, besides Penrose, expects the Universe to be a fractal? Especially as in the Planck scale of length it must be more or less discrete. Friendly Neighbour 12:28, 4 September 2006 (UTC)

There is no a priori reason why the universe couldn't start in a fractal state. I thing physicists have a bias towards smooth things--(piece-wise-) continuous functions, smooth manifolds, etc. Why should nature be like this? I think one should provide a good argument why the initial state should not be fractal. I'm speculating that in some sense non-fractals form a measure-zero subset of "all sets." I can see why Penrose, being a mathematician, may have a totally different perspective on things.-- Bartosz 02:54, 6 September 2006 (UTC)

I see no way the Universe may have (now or in the begining) a fractal state if you cannot have any structures smaller than the Planck length. Fractals are impossible if you are length scale limited. It seems Penrose (whose idea this is) really does not believe in quantum mechanics. Friendly Neighbour 09:19, 6 September 2006 (UTC)

This is a circular argument. The only rationale against structures smaller than the Planck length that I know of are based on the assumption that the current theories are still valid at such distances--which we know they aren't. Am I wrong?-- Bartosz 21:05, 6 September 2006 (UTC)

Still, the burden of proof in on those who say the known laws of physics (especially Heisenberg uncertainty principle) are not valid at the Planck length scale. Otherwise, you could as well say that I use a circular argument doubting that that the Universe at the Planck scale is inhabited by garden gnomes. The only rationale against Planck gnomes is based -- according to your rationale -- on the assumption that known laws of physics hold at the distance. Friendly Neighbour 06:00, 7 September 2006 (UTC)

How does Heisenberg uncertainty principle preclude structures below Planck scale? It precludes mesuring them (for instance, by Planck gnomes), but not their existence (whatever we mean by "existence" at such extreme conditions where no measurements are even imaginable) . After enough stretching by inflation, these structures could have become measurable. -- Bartosz 19:52, 7 September 2006 (UTC)

The same way it limits the diameter of a proton, atom nucleus or the minimal size of electon orbits. It's a popular misconception that a measurement is needed for the Heisenberg uncertainty principle to start working. Actually, the article on the principle explains the misconception in the section titled "Common incorrect explanation of the uncertainty principle". This is actually one of the fundaments of quantum mechanics. See for example "Common Misconceptions Regarding Quantum Mechanics" by Daniel F. Styer, especially sections III.8 & III.9. Friendly Neighbour 20:10, 7 September 2006 (UTC)

I am not arguing for the hidden variable interpretation, which is being alluded to in the article you're quoting. I just don't know of any physical argument that would eliminate wave functions whose wavelength is shorter than the Planck scale. -- Bartosz 18:22, 8 September 2006 (UTC)

You said that Heisenberg uncertainty concerns measuring, not existence - and this is exactly the same thing as stating that hidden parameters do exist. Let's stop this nonsense. Planck length is the lower limit of meaningful physics due to this very uncertainty. If a particle is smaller than the length, it has enough momentum (and hence energy) to create virtual black holes. Its energy uncertainty is larger than its rest mass and this makes the concept of particle unclear. This i what make the concept of string (in place of point particles) so compelling. I'll stop responding here leaving you with a whole article on the subject: arXiv:gr-qc/9403008. Friendly Neighbour 20:00, 8 September 2006 (UTC)

The article predictably speaks about measurements. From the abstract: "The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity." Obviously no measurements were possible during the inflationary era. So to me your argument sounds like this: In the pre-inflationary universe one could not make any measurements that would involve scales smaller than the Planck scale; therefore, when one makes measurements now, one cannot measure traces of any structures that would correspond to sub-Planck scales back then. I just don't see the connection. I think it's more a matter of intuition than strict science, so we are probably stuck until a better theory arrives.-- Bartosz 00:52, 9 September 2006 (UTC)

The fractal claim was bizarre and best removed. However I'm having problems understanding both the problem as described by Page/Penrose and Davies' rebuttal:

I don't understand the Page/Penrose clause "thermalization at the beginning of the inflation era pushes the initial entropy even lower". Perhaps this could be explained a bit more clearly / less concisely?

In the Davies rebuttal what does "a very low entropy value -- due to random quantum fluctuations -- to account for the observed thermodynamic arrow of time" mean? That the "random quantum fluctuations" drove down the entropy ? Most unlikely. Or that the entropy had to be low to "eliminate" the field fluctuations which would otherwise prevent inflation from starting? More likely. But then Davies' argument is a purely anthropic one. Surely we can do better than this? I'd reword it myself but the Davies ref doesn't appear to be available online so I can't see if this was what he meant. --Michael C. Price ^talk 10:28, 5 September 2006 (UTC)

I copy-edited the section to accomodate some of the comments (the middle paragraph above). The sentence about thermaliazation was not mine - it was written by the original author of the section (User:Bartosz). I hope it is now easier to understand. I also corrected the moment of thermalization (reheating) which in fact had to happen at the end of the inflation, not in its initial stage. I'll change the word to reheating in my next edit. Friendly Neighbour 11:56, 5 September 2006 (UTC)

Now, on the random fluctuation sentence. You have a point here. I used a rendition of his argument from Albrecht & Sorbo 2004: "The position we take here (which was suggested by Davies [...]) is basic acceptance of this point. If you can regard the big bang as a fluctuation in a larger system it must be an exceedingly rare one to account for the observed thermodynamic arrow of time. Also, we believe that this is the most attractive possibility for a theory of initial conditions. Other theories of initial conditions seem to us more ad hoc, and less compelling.". This is a purely anthropic idea. I have access to the Davies paper as well. Re-reading it now I'm not sure that Davies was basing his argument on the principle only. More on that soon. Friendly Neighbour 12:33, 5 September 2006 (UTC)

OK, I've re-read Davies 1984. The first time was really cursory and it seemed to confirm what I read in Albrecht & Sorbo 2004. Therefore I chose the text from the latter article as the idea was more compacted and focused in their short rendering. The original Davies article considers two scenarios of inflation origin which seemed feasible at the time. One is tunneling from "nothing" in which case "inflation merely acts to drastically reduce the improbability of such a state by permitting a wide class of initial staes to develop into something like the universe we now see". The other scenario involves inflation which starts from a fluctuation of a "pre-existing Friedman-like phase". In this case "one can accept an arbitrary initial state but appeal to anthropic selection of an atypical region". This is the case Albrecht and Sorbo talked about, most probably because tunneling from nothing isn't now as popular as was in 1984.

I'll add that a quantum fluctuation can easily decrease locally entropy. Entropy grows only globally. For example, we are living examples of local entropy decrease. Of course, the world pays an entropy price for our existence. Friendly Neighbour 13:29, 5 September 2006 (UTC)

Albrecht & Sorbo 2004 is a great link that you gave. Indeed I suggest replacing Davies' argument altogther with Albrecht & Sorbo's. Howabout:

In fact the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state, compared with a non-inflationary cosmos overwhelming favours the inflationary scenario[4], simply because the amount of "seed" required for the inflationary cosmos is so much less than any non-inflationary alternative.

What do you think? --Michael C. Price ^talk 17:44, 5 September 2006 (UTC)

I definitely like it. Fire when ready ;-) Friendly Neighbour 19:11, 5 September 2006 (UTC)

Great, I see you've found a "proper" ref for it. --Michael C. Price ^talk 19:55, 5 September 2006 (UTC)

This whole field is widely speculative, so I don't think one should use statements that suggest some kind of strictness of argument.

"In fact the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state, compared with a non-inflationary cosmos overwhelming favours the inflationary scenario, simply because the amount of "seed" required for the inflationary cosmos is so much less than any non-inflationary alternative."

One can talk of probability only within a certain framework that defines the space of possibilities. We have no agreed framework for eveluating pre-big-bang states. What "seed" are we talking about and how do we measure its amount?

I suggest you download the PDF article for these details. --Michael C. Price ^talk 07:00, 6 September 2006 (UTC)

If nobody protests, I'll remove this sentence.

My understanding of the original criticism of inflation is that it tries to solve what is perceived as a problem by exaggerating another problem. Why do two remote regions of the universe have the same temperature? It could be because they started at the same temperature, or because they had time to exchange heat. Inflation is based on the premise that it is unreasonable for the universe to start in a uniform state, therefore there had to be a thermalization period. But the non-uniform state has lower entropy than the uniform state. One might say that it's even more unreasonable to assume such low entropy for the initial state. I'm not saying I buy that argument, but I see the point.

Bartosz 23:53, 5 September 2006 (UTC)

This isn't quite a fair shake for the theory. Inflation developed with the understanding that the horizon problem was difficult to resolve using "standard" cosmology, but Linde wasn't looking for a patchwork for this. It just happens that a scalar field inflates. There really is nothing more to it than that. Highly symmetrical universes inflate as a general rule: the theoretical exception are those models which do not have a kind of inflation. To this end, inflation is not a cart-before-the-horse proposition at all, it is a fully "organic" result of the simplification of physics at high densities and pressures. --ScienceApologist 00:14, 6 September 2006 (UTC)

I'm not sure which is cart and which is horse. Universes with a cosmological constant inflate, but they never stop. Scalar fields and phase transitions are still very speculative (meaning, we haven't seen a Higgs yet, and there is no accepted GUT). So present-day particle physics offers little support for inflation. In general, I'm a little worried about the whole article giving the wrong impression to non-specialists about what is solid science and what is speculation. According to Penrose, physics before 10^-1s after the Big Bang is speculative and I think this is a good ballpark. -- Bartosz 01:47, 6 September 2006 (UTC)

The article clearly states that the particles physics is speculative. However the astrophysical reasoning is quite sound. Inflation is now understood as a generic property of various theories (indeed most theories) and is not arm-waving. --Michael C. Price ^talk 07:00, 6 September 2006 (UTC)

Penrose, in the best tradition of skittish scientists, is being overly conservative with his characterizations and ignores/is unaware of the astrophysical evidence. WMAP, after all, has firmly established an inflationary universe in a very clever way. It's a bit arbitrary for Penrose to make a 10^-1s cut-off for parameterizing ignorance. Obviously he's more comfortable with nucleosynthesis than he is with baryogenesis, but this may be due to sour grapes since his early universe theories fell rather flat. In particular, the detail parameterization of inflation is well-understood from the observational evidence and the generic quality of inflationary models (it doesn't matter what kind of GUT is correct, it just matters that the physics follows the currently observed trend of becoming more and more symmetrical at higher energies). ScienceApologist 12:28, 6 September 2006 (UTC)

Friendly Neighbour says: "I also corrected the moment of thermalization (reheating) which in fact had to happen at the end of the inflation, not in its initial stage. I'll change the word to reheating in my next edit."

I may be wrong, but my understanding is that the thermalization happened at the beginning and not at the end of inflation (also, it is not the same as "reheating"). In an exponentially expanding universe, the distances between points increased very slowly at the beginning, then accellerated very rapidly (an exponential curve always starts slowly). Heat exchange could only take place in the slow phase. Compare it with the non-inflationary solutions, where the expansion is the fastest at the beginning, precluding any exchange of heat. —The preceding unsigned comment was added by Bartosz (talk • contribs) .

You are wrong, thermalisation occurs at the end of inflation, when the inflaton field decays into an array of other particles. Whilst inflation is in progress this decay (and the associated temperature rise) is supressed. That's why it is called "reheating". --Michael C. Price ^talk 07:00, 6 September 2006 (UTC)

I think that Bartosz was talking about equilibration which is a generic property of inflating regions -- but it doesn't just deal with temperature -- EVERYTHING equilibrates. During inflation, temperature is an ill-defined measurement, that's why reheating is so interesting. --ScienceApologist 12:32, 6 September 2006 (UTC)

Well, he used the term "thermalization". Friendly Neighbour 12:41, 6 September 2006 (UTC)

My understanding is that exponential expansion started off slowly, so the whole region that later became the visible universe, had enough time to reach thermal equilibrium. At the end of the inflation, this region was already too big and expanding too fast to allow for heat transfer between its far ends. -- Bartosz 19:52, 7 September 2006 (UTC)

Inflation does have its problems (as any new theory is expected to have). They are nicely resumed in Brandenberger 2001 (linked also from the article page). Arrow of time is not even mentioned there as it is a recent rehash of an old argument from 1980s (see above for details). Therefore, we should either beef up the Criticism section (renaming it to something like "Problems of Cosmic Inflation") or maybe delete it completely as it now focuses only on an obscure argument about something which is not even a central concept of the theory (and IMHO the arrow of time discussion is anyway more in the realm of philosophy than physics, anyway). What do you think? Friendly Neighbour 09:04, 6 September 2006 (UTC)

It is not an obscure argument in the public / pop' science domain -- I've seen it referred to in various forms in the last decade (usually citing Penrose as source) -- so it definitely has a place here. (I don't agree that the arrow of time is a philosophical issue -- although most philosophers lack sufficient grounding in thermodynamics to be able to discuss it with any competence.) As for what to do with the criticism section, I agree: either more problems should be included (e.g. lack of firm Higgs data) or the title changed. --Michael C. Price ^talk 11:11, 6 September 2006 (UTC)

Arrow of time question in Cosmic inflation

Caveat: this opinion of mine is an off-topic philosopical opinion and does not cover to the question of what to do with the section:

I knew someone will react :-) But I'm quite serious. If you think for example about the demarcation criterion proposed by Karl Popper, what possible machanism of falsifying the connection of the arrow of time with entropy can one offer? Even as I am not quite a fan of Popper, I see a problem here. If there is no way (and by possible I don't mean technically feasible but not breaking any laws of logic and physics ruling our Universe) of testing a hypothesis, then it is not physics. It's philosophy. (I'm not sure whether Popper was aware that philosophy is not science according to his own solution of the demarcation problem but it obviously isn't). Friendly Neighbour 12:07, 6 September 2006 (UTC)

Thermodynamics has a lot of overlap with information theory, the latter which has theorems which are tautologically provable rather then empirically provable. I suspect that the thermodynamics / arrow of time issue lies within this tautological domain. --Michael C. Price ^talk 14:25, 6 September 2006 (UTC)

We go a looong way off-topic here but I can't resist replying ;-) I do not agree that thermodynamics is not experimentally testable. You test it every time you start the engine in your car. You test it every time you have to heat the water to boil it instead of waiting until decreasing entropy does it spontaneously. Etc. etc. It's the thermodynamics <-> time arrow conection which is, in my opinion, physically non-testable. Simply because thermodymanics has the only law we know that is not time reversible (except for the charge-parity symmetry which is somehow a less popular "source" of the arrow of time), people connect the two together. In fact there is no evidence that CP symmetry, some yet unknown law of physics or even nothing at all is the reason time goes in the direction we observe (if it does at all). I'll have yet to finish "The Fabric of the Cosmos: Space, Time, and the Texture of Reality" by Brian Greene but I doubt that even he can convince me about the importance of the connection. Friendly Neighbour 14:58, 6 September 2006 (UTC)

Just to correct a missimpression I seem to have made - not all thermodynamics is tautological (I think we agree on this): just the overlap with information theory.

It's a fun subject, and not entirely off-topic, since inflation - arguably - is the "source" of the universe's free-energy. I remember attending a talk by Davies c1981 where he argued precisely this point. I say "precisely", although I have forgotten the details :-( ; something to do with inflation creating the gap between the universe's actual entropy and the maximum possible entropy. But the talk included the claim that inflation had finally "explained" the arrow of time. I'll have to dig around and see if he wrote anything on the subject. --Michael C. Price ^talk 16:21, 6 September 2006 (UTC)

I'll also read today, if time allows, (pun intended) the paper (Milan M. Cirkovic "The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument", Foundations of Physics, 33, 3, March 2003) whose author claims in the abstract that he showed "that there is a third possible alternative, based on the generalization of the classical (‘‘Boltzmann–Schuetz’’) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann’s statistical measure at its face value, and accomodating it within the quantum cosmological concept of the multiverse. ". But that's exactly what I was afraid of. You have to create a Multiverse to test experimentally the concept ;-) Friendly Neighbour 16:43, 6 September 2006 (UTC)

OK, Cirkovic thinks he invented the anthropic Multiverse reason of growing entropy (life is possible only in universes where it increases). In fact Davies in his 1984 article used it, though not as expliciotely. I'm still not sure why people think that explaining the growing entropy explains also the direction of time.

By the way, Hawking had a hillarious paper on the subject (Hawking, 1985, "Arrow of time in cosmology", Phys. Rev. D 32, 10, 2489-2495). He thought that in a collapsing universe or close to a black hole the entropy would fall. He even proposed an experimental test involving a black hole! However, in a long note added after the review he thanks Don Page for showing that the expected entropy decrease is not true. Hawking still saw two points of his paper that remained correct. The second one (that a universe started with inflation will have a well defined arrow of time!) is never mentioned in the article itself. How bizarre. I wonder why he didn't retract the whole thing. Friendly Neighbour 19:00, 6 September 2006 (UTC)

Is that the same paper where Hawking predicts that time will flow backward when/if the universe starts to contract? A real clanger!

Well, he was cautious enough to use the term "thermodynamical arrow of time" everywhere in the article, defining it as "the direction of time in which entropy increases". Therefore I read his contracting universe prediction simply as "entropy will decrease" (I cannot grasp the alledged reason why time flow will follow entropy) and some people understand it as "time will reverse" which is not necessary the same. Friendly Neighbour 19:58, 6 September 2006 (UTC)

I guess the reason why people think that the entropy gradient defines the arrow of time is that we have the Planck-Boltzmann law $S=k\log \Omega$. Number of microstates $\Omega$ correlates with the entropy S. Thus we can define a one-to-many relationship between the macrostates in the past with the macrostates in the future, by the appropriate grouping or microsates into macrostates. Hence we can remember the past because we can define a unique macrostate for it, but there is too much choice for the future. There are many other ways of expressing this of course. --Michael C. Price ^talk 19:38, 6 September 2006 (UTC)

I have a gut feeling that this is exactly where philosophy starts. Friendly Neighbour 19:58, 6 September 2006 (UTC)

I feel the same way about anthropic based arguments. --Michael C. Price ^talk 20:22, 6 September 2006 (UTC)

Generally, from what I read today there are three explanations of the "thermodynamic arrow of time":

• statistical laws say so - the entropy must grow (for me the most sound, for most persons involved a lame argument),
• initial conditions of low entropy - for accident by a random quantum fluctuation before the inflation (inflation does make it much easier to imagine this "accident"),
• the anthropic principle - in fact a variant of the second argument, just adding the fact that otherwise we would not live to observe the universe.

I do not like the anthropic principle too much. For me the first explanation is good enough. if, not inflation makes me easier to imagine the random fluctuation that created our freak universe. But some people prefer to think in the anthropic way. So be it. Friendly Neighbour 20:42, 6 September 2006 (UTC)

For me the statistical argument is weak because the same logic that dictates that $S(t_{n+1})\geq S(t_{n})$ also implies $S(t_{n-1})\geq S(t_{n})$. So, if we don't like the anthropic principle, we are left with only the initial conditions argument. --Michael C. Price ^talk 00:18, 7 September 2006 (UTC)

For a not so philosophical attempt you may want to read hep-th/0301115 by Detlev Buchholz. --Pjacobi 20:11, 6 September 2006 (UTC)

Thanks for adding one more arrow of time. A "relativistic quantum timelike cone arrow of time"? Friendly Neighbour 20:42, 6 September 2006 (UTC)

Edits by User:Bhenderson

A new user continues to make edits to this page that are slightly problematic. The prose he includes doesn't add any substantive information to the article and introduce a misconcpetion that inflation accounts for the current scale of the universe (which it doesn't because expansion is still occuring). --ScienceApologist 15:57, 10 September 2006 (UTC)

Some more sources on cosmic inflation and the arrow of time

I've found some more sources we could use:

1. Sean M. Carroll, Jennifer Chen, 2004 "Spontaneous Inflation and the Origin of the Arrow of Time", hep-th/0410270
2. Sean M. Carroll, Jennifer Chen, 2005, "Does Inflation Provide Natural Initial Conditions for the Universe?", gr-qc/0505037
3. Robert M. Wald, 2005, "The Arrow of Time and the Initial Conditions of the Universe", gr-qc/0507094

The first two papers claim to have explained why "spontaneous eternal inflation can provide a natural explanation for the thermodynamic arrow of time" and why "a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time". The third paper argues that "it is not plausible that these special initial conditions have a dynamical origin" or to put it plainly does not believe that inflation explains why the universe had to start in a low entropy state. Friendly Neighbour 18:30, 27 September 2006 (UTC)

Questions and edits regarding usage of Inflaton in first pararagraph

I recently made an edit to the sentence in the first paragraph, to generalize usage of the term Inflaton, which made it more closely reflect Wikipedia's entry. I also inserted the word believed (possibly mis-spelled), and it was recently deleted. Is there a clear consensus with this body of editors, regarding whether the Scalar field (or constant B-field) referred to as the Inflaton is regarded as a fact? I thought that; at this point it is considered an abstraction which is convenient in String Theory and M-Theory, to account for the observed properties of Cosmic Inflation. I would like to state that there are some perfectly reasonable Inflationary Universe theories currently being considered, which do not employ the Inflaton. It seems a bit gratuitous to present it as a fact, therefore. JonathanD 16:42, 12 October 2006 (UTC)

Well, the scalar field has been the standard way to discuss inflation since Guth. So it is a pretty accepted part of inflation theory – which is not to say that if inflation ultimately turns out to be correct, it has to be governed by a scalar field, because inflation only means a short, de Sitter-like epoch in the early universe. There are a few attempts at inflation without additional scalar fields, namely Starobinsky's early work suggesting that inflation arose in the early universe from quantum corrections to gravity, and Dirac-Born-Infeld inflation in string theory, in which the role of the inflaton is played by the position of a D-brane (which can be thought of as a scalar field, but not simply). But I would say that having a scalar inflaton is much less controversial than inflation itself.

As for how widely inflation is believed, well, the predictions of inflation have been very accurately confirmed, so any successor will have to make the same predictions. On the other hand, the theory itself is on somewhat shaky ground. I think most people believe that the basic picture works, but that the theory might still have some surprises in store. –Joke 19:48, 12 October 2006 (UTC)

Is there not also "vector inflation" where the inflaton is not a scalar field but a -- surprise, surprise -- vector field, without recourse to string theory or quantum gravity?

How long?

The overview states:

"It is not known how long inflation lasted but it is thought to be extremely short. "

But what about the possibility of eternal inflation? --Michael C. Price ^talk 08:51, 13 October 2006 (UTC)

I changed the wording of this slightly. Although inflation didn't happen for very long in terms of today's timescales, it lasted for many Hubble times and therefore was a pretty long event in the grand scheme of things up until that point. Since eternal inflation depends on higher potential false vacuums, I think we can safely assume we are talking about the latest round of vacuum decay rather than the infinite regression of vacuum decays that may or may have not happened in the past. --ScienceApologist 01:04, 15 October 2006 (UTC)

It still doesn't address the eternal inflation possibility which, AFAIK, does not depend exclusively "on higher potential false vacuums". Until the nature of the inflaton is discerned we should be open to the possibilty that the latest round of inflation may have been both chaotic and eternal -- i.e. of indefinite duration. --Michael C. Price ^talk 08:19, 15 October 2006 (UTC)

Even if it is eternal to both the past and future, it is still possible that any given worldline is finite and of short duration (compared to, say, a second). I think this is what actually happens, but can't say for sure (and even if I could that would be OR). So while inflation is eternal, a worldline chosen at random has a finite expected proper length. This is like how in probability theory an unbounded positive random variable can still have finite expectation value.

On a broader note, this is a common statement in the popular and technical literature. It can be interpreted most simply to mean that the last sixty e-folds last a very short time. –Joke 01:20, 16 October 2006 (UTC)

For a world line starting during eternal inflation and going forward in time the proper inflationary time would be short time, but what about a world line projected back in time? Wouldn't that be of indefinite duration? --Michael C. Price ^talk 06:52, 16 October 2006 (UTC)

I was basing my comments on the comment above from an IP anon:

Dr. Linde does discuss in this paper his opinion that even though any particular past-directed geodesic must have finite length, there is no reason to conclude that there must be an upper limit on that length, so inflation can be eternal in the past.

So according to this statement, every past-directed geodesic ends eventually. I really don't know what to say beyond this – I had thought that the Borde-Guth-Vilenkin argument was universally accepted until I saw this discussion. –Joke 01:59, 17 October 2006 (UTC)

Yes, according to that statement every past-directed geodesic ends eventually -- but that is precisely what we are not discussing . We are discussing whether it must end within any particular definite period -- and the answer is that it need not. --Michael C. Price ^talk 02:18, 17 October 2006 (UTC)

Well, it's a bit of a stretch to say that it is precisely what we were not discussing. Of course the length of a worldline can be unbounded (in future-eternal inflation that is true too). But still, a typical worldline has a very short proper length (again, compared to say, one second). –Joke 02:38, 17 October 2006 (UTC)

With eternal inflation a typical worldline has a short future proper length but an unbounded proper length to the past. --Michael C. Price ^talk 09:01, 17 October 2006 (UTC)

Hmm, perhaps this can all be resolved if we state that the inflationary epoch lasted on the order of 10^-30 seconds (being 100s if not 1000s of times more generous), but that it lasted for many Hubble times. After all, it's the inflationary epoch that people usually describe as "inflation". Chaotic/eternal inflation involves other inflationary epochs that occur at other earlier/later times.

How do we know that the lastest, and perhaps only, period of inflation wasn't chaotic/eternal? --Michael C. Price ^talk 14:01, 17 October 2006 (UTC)

Depends on whether you think the Hubble parameter was bounded or not. Most inflationary models require it to be constant. If this is true than inflation has a beginning and an end. Models that include a changing Hubble parameter are still bound by the peculiar effect that the flatness of inflation chooses a lower-bound for the Hubble parameter. In effect, an inflating solution to the Einstein equations prevents eternal past-worldlines from existing in our universe because when you assume they exist they simply do not show up for similar reasons that there are no point defects. I have yet to see a contradiction to this.--ScienceApologist 07:30, 18 October 2006 (UTC)

I don't understand the "point defects" reference. Could you explain more? Do you refer to the Borde-Guth-Vilenkin singularity argument? --Michael C. Price ^talk 07:59, 18 October 2006 (UTC)

Yes, and more. A bounded Hubble parameter implies that inflation had to "start" for most worldlines. Vilenkin wrote a number of papers about this. --71.57.90.3 00:54, 20 October 2006 (UTC)

Which have been superseded by past eternal inflationary models which are singularity free and geodesically complete:. --Michael C. Price ^talk 06:22, 20 October 2006 (UTC)

However, in both of these papers, the question that's being asked isn't "are all worldlines infinite?" but rather "does there exist an infinite worldline?" These articles do not supercede the general point that point defects reign supreme as you go back to conformal times where the universe is less inflated. --ScienceApologist 12:35, 20 October 2006 (UTC)

No, the main question being asked "Have we circumvented the restrictions implied by "Borde Guth Vilenkin", which they reference, and the answer is yes. They have constructed a steady state, past and future eternal inflationary scenario. --Michael C. Price ^talk 12:43, 20 October 2006 (UTC)

Not clear that the answer is as baldly "yes" as you are claiming it to be. In fact, these papers admit that their volumes that contain bundles of infinite worldlines asymptotically approach zero for the total universe. While they also propose some cosmetic fixes for this problem, what we ultimately have is BGV coming back to haunt the authors as they try to avoid it. --ScienceApologist 13:21, 20 October 2006 (UTC)

No, it is quite simple. The BGV worldlines from "I" simply cross over into "II", and vice versa. --Michael C. Price ^talk 14:14, 20 October 2006 (UTC)

That's the idea, but there is no attempt to describe how many worldlines actually end up in I in the first place. But that's okay because they didn't set out to prove this as a statistical argument: only a possibility argument (as I've been stating all along). --ScienceApologist 18:35, 20 October 2006 (UTC)

I disagree with your original research, but it's irrelevant anyway: the possibility that their steady state eternal inflation model is correct is enough to refute the statement that we would expect the period of past inflation to be short. --Michael C. Price ^talk 02:39, 21 October 2006 (UTC)

As I've been saying all along, there is no contradiction in something having unbounded length to the past but having the expected length short. Certainly the length to the future is unbounded (but also has quite short expected length) in any eternal inflation scenario. –Joke 13:34, 17 October 2006 (UTC)

Just because there's no contradiction with your statement doesn't mean it's either true or appropriate for the article. There are too many theories about inflation, with insufficient empirical grounding to distinguish amongst them, to state that the period of inflation was "short". All we can say is that is there is a minimum period/amount of inflation required to resolve various astrophysical conundrums. --Michael C. Price ^talk 14:01, 17 October 2006 (UTC)

OK, fine, but all existing theories of inflation have inflation last a short period. The Hubble time is essentially the only physical parameter during inflation, and it sets the timescale. Inflation lasts many Hubble times, but even if it lasts a billion Hubble times, it is still short. Yesterday I changed the phrasing to "usually thought to be extremely short compared to today's timescales" which is so equivocal that surely everybody can be satisfied? –Joke 14:29, 17 October 2006 (UTC)

The wording is better, but I'm still having problems reconciling the use of "short" with "unbounded". At the very least the article looks inconsistent, saying that the period of inflation is thought to be short and then discussing eternal inflation: "New inflation is generally eternal: that is, the process continues forever." BTW my previous question "How do we know that the lastest, and perhaps only, period of inflation wasn't chaotic/eternal? " remains unanswered. --Michael C. Price ^talk 15:00, 17 October 2006 (UTC)

Current expectation is that it is both chaotic and eternal. Here is the picture: take an ensemble of worldlines in an eternally inflating universe. The end of inflation occurs somewhat like radioactive decay: it has an exponential distribution with finite expected time τ until the end of inflation. So inflation has ended on about half (really 1-1/e) of the worldlines after time τ. However, the space around the remaining worldlines has expanded so dramatically that you can't really say that less of the universe is inflating. It is the weird paradox of eternal inflation: any given observer (such as ourselves) experiences inflation for only a short time, while the universe as a whole inflates indefinitely. It is another one of these strange problems of gravitational gauge fixing, Bayesian proability and the anthropic principle and has been causing people a lot of grief defining anything sensible in the string landscape, for example. –Joke 15:53, 17 October 2006 (UTC)

That's fine, I have no problem with that explanation. It explains why a typical observer would expect inflation to end within a short period, but it does not explain, or give any reason to expect, the past of the same world line(s) would have experienced inflation for a similarly brief period. --Michael C. Price ^talk 18:00, 17 October 2006 (UTC)

What you are arguing is essentially akin to arguing that it is possible to win the lottery and prove the Second Law of Thermodynamics incorrect. While technically the statistics don't forbid you from having a worldline that is eternal, the probability of such a thing is so vanishingly small as to be as impossible as seeing a glass spontaneously reassemble by having every particle tunnel into the appropriate arrangement. Just not going to happen. --ScienceApologist 07:36, 18 October 2006 (UTC)

No, eternal inflation forms a tree-like (almost fractal) structure with the branches pointing forward in time. A typical worldline terminates quite soon (for the reason given by the radioactive decay analogy). But tracing the same worldlines backwards simply moves to older sections of the trunk. --Michael C. Price ^talk 07:52, 18 October 2006 (UTC)

Let's try another tack, and call the moment when eternal/chaotic inflation kicks off t=0. What is the expected value of t (i.e. the period of past inflation) for a typical observer? t is larger than any finite value, since there is more(*) "volume" (inflating and post-inflating) to the future than to the past of any space-like hypersurface. (*"More" because there is only a finite amount to the past, an unbounded, infinite amount to the future.) Ergo the expected duration of past eternal inflation is infinite -- or at least very, very large, probably unbounded and certainly not "short" by any stretch of the imagination, by any Bayesian computation.

PS this picture does not conflict with the second law of thermodynamics since entropy is always increasing with time. --Michael C. Price ^talk 10:41, 18 October 2006 (UTC)

You're missing the point of the analogy. It's not to say that your view violated the second law of thermodynamics; it's to say that your counter-example to brief inflation is so entirely unlikely as to be impossible. --71.57.90.3 00:50, 20 October 2006 (UTC)

And you're missing the point that references already in the article support past eternal inflation.

No, I'm pretty sure I understand what they are saying. There doesn't seem to be a contradiction in stating that a single worldline may be infinite but may also be impossible to find. --ScienceApologist 12:35, 20 October 2006 (UTC)

No, all geodesic wordlines are proper time infinite in their construction. They would hardly call it steady state, past eternal inflation otherwise -- and not just in passing but all the way through both articles. Look at the conformal diagrams. --Michael C. Price ^talk 12:40, 20 October 2006 (UTC)

Here's one of the abstracts. It's pretty unambiguous:

Since the advent of inflation, several theorems have been proven suggesting that although inflation can (and generically does) continue eternally into the future, it cannot be extended eternally into the past to create a "steady-state" model with no initial time. Here we provide a construction that circumvents these theorems and allows a self-consistent, geodesically complete, and physically sensible steady-state eternally inflating universe, based on the flat slicing of de Sitter space. This construction could be used as the background space-time for creation events that form big-bang-like regions, and hence could form the basis for a cosmology that is compatible with observations and yet which avoids an initial singularity or beginning of time.

--Michael C. Price ^talk 12:52, 20 October 2006 (UTC)

I just reread the papers. The construction they are talking about in the paper you cite is essentially arguing that in their unique form of double-well inflation, the global symmetries of inflating spacetime admit some geodesics that are infinite (highlighted in their conformal diagrams). This I don't argue with, but BGV never said anything about there not being any infinite geodesics, it said (essentially) that the probability of finding such a geodesic is zero given the eternal nature of inflation. The authors are careful to avoid saying that they disproved BGV, but instead argue that their construction has the possibility to avoid singularities. However, they don't give any indication of how likely it is to do this and are clear that there are worldlines in their models which do not have this feature. --ScienceApologist 13:21, 20 October 2006 (UTC)

Their models are not dependent on their "unique form of double-well inflation", but would appear in any eternal inflation model --- which is most of forms inflation we are interested in. As for how probable their model is -- well that is speculative, of course, as are all models of inflation.--Michael C. Price ^talk 14:18, 20 October 2006 (UTC)

The relevant point to note is that the beginning of inflation in the model is infinitely in the past of the typical observer ($t=-\infty$ in their diagrams). Hence claiming that inflation in our past was "short" is not correct. --Michael C. Price ^talk 14:43, 20 October 2006 (UTC)

No, they make no claims on the "typical" observer. They make claims on the existence of an observer who sees such a thing. But that observer has to be in a special part of their model: a part that is emphasized by their choice of conformal diagram, but isn't rigorously shown to be the most probable worldline. And they admit that there are worldlines in their model which are not infinite so the point I'm making stands. --ScienceApologist 18:35, 20 October 2006 (UTC)

Again, I disagree with your original research (they do mention the randomly choosen observer in the context of the PCP which they claim is adhered to in their model), but it's irrelevant anyway: the possibility that their steady state eternal inflation model is correct is enough to refute the statement that we would expect the period of past inflation to be short. That statment only applied to the original "old" and "new" inflation which predates the chaotic eternal models. --Michael C. Price ^talk 02:39, 21 October 2006 (UTC)

My understanding is that it would be exactly the same thing going into the past, except that you would run into singularities, not reheating. –Joke 00:46, 18 October 2006 (UTC)

There's no connection between the two timescales, they are simply different physical processes. Think about the radioactive analogy: the decay time of an isotope has no connection to the formation time of the same isotope. This simply so obvious that I don't what else to say. --Michael C. Price ^talk 05:56, 18 October 2006 (UTC)

That's a priori true, but there is only one timescale during inflation: the Hubble time. So both the time for the end of inflation and the time for the formation of singularities must be related to it in a straightforward way. It's a simple case of dimensional analysis. –Joke 14:04, 18 October 2006 (UTC)

By the same argument the universe would never be able to inflate beyond its Hubble distance -- yet it does; that's the whole point of inflation. --Michael C. Price ^talk 15:11, 18 October 2006 (UTC)

No, these are rough estimates. There are other dimensionless constants, such as the slow-roll parameters (ε and η) and H/m_Pl that occur in the expressions for these dynamical timescales. But none of these constants are going to change 10⁻³³ seconds to one second unless some incredible fine-tuning occurs. –Joke 15:41, 18 October 2006 (UTC)

Sorry, I must have missed the explanation of why your dimensional argument applies to the Hubble time but not the Hubble distance. Anyway this is all besides the point: a dimensional argument wouldn't prevent the inflationary past duration from being infinite (see above). --Michael C. Price ^talk 15:51, 18 October 2006 (UTC)

possibility that their steady state eternal inflation model is correct is enough to refute the statement that we would expect the period of past inflation to be short. -- No it's not enough to refute the statement. It's the opinion of a single pair of researchers. Joke is right, it's "usually" considered short. --ScienceApologist 02:54, 21 October 2006 (UTC)

You forgot to include Linde. So that's three. And I haven't started searching yet. BTW minority views are still reported on Wikipedia and any claim that it is a minority view will need backing up with references. --Michael C. Price ^talk 03:08, 21 October 2006 (UTC)

Linde doesn't talk much these days about eternal inflation, but even so his version was much more of the phase transitions being eternal rather than having one smoothly inflating de Sitter space back to negative infinity. --ScienceApologist 17:13, 21 October 2006 (UTC)

Hmmmm. Linde notes in a 2005 review that eternal inflation's pretty mainstream nowadays, with past eternal inflation an open question[5]. --Michael C. Price ^talk 19:23, 21 October 2006 (UTC)

Yeah, I remember that paper. I think it illustrates well the point Joke and I are making. --ScienceApologist 12:47, 22 October 2006 (UTC)

It illustrates is that you and Joke do not have a good grasp of chaotic eternal inflation, since you claimed it violates the 2nd Law and Joke claimed it to be in conflict with "simple" dimensional analysis. --Michael C. Price ^talk 13:28, 22 October 2006 (UTC)

I never claimed it violated the 2nd Law of Thermodynamics. That's insulting and disingenuous, Michael. Stop the self-aggrandizing and come back to the discussion. --ScienceApologist 16:34, 22 October 2006 (UTC)

You claimed that my argument about eternal inflation not implying a short period of historical inflation was "essentially akin to arguing that it is possible to win the lottery and prove the Second Law of Thermodynamics incorrect." Personally I found that pretty insulting. --Michael C. Price ^talk 17:30, 22 October 2006 (UTC)

Interesting that you would find it insulting since what I was comparing your argument to is a valid discussion from statistical mechanics. I find your argument and supporting evidence to be missing the forest for the trees, as it were. Technically correct but statistically unlikely. It's a matter of whether you think the question should be "does an infinite worldline exist?" or "are infinite worldlines the most common?"--ScienceApologist 01:16, 23 October 2006 (UTC)

I also note that neither of you have responded to the argument that the Bayesian-expected length of past inflation is unbounded or infinite: call the moment when eternal/chaotic inflation kicks off t=0. What is the expected value of t (i.e. the period of past inflation) for a typical observer? t is larger than any finite value, since there is more(*) "volume" (inflating and thermalised) to the future than to the past of any space-like hypersurface. (*"More" because there is only a finite volume to the past but an unbounded, infinite volume to the future.) Ergo the expected duration of past eternal inflation is infinite -- or at least very, very large, probably unbounded and certainly not "short". --Michael C. Price ^talk 13:28, 22 October 2006 (UTC)

This ignores the fact that phase transitions result in an uncountably infinite number of singularities in many eternal inflation models. So the density of singularities prevents most worldlines in those models from being unbounded/infinite. --ScienceApologist 16:34, 22 October 2006 (UTC)

That is not BGV's argument about proper-time-past-incomplete geodesics, which only presents putative problems at time $t=-\infty$. If you have a verifiably sourced argument that demonstrates that past inflation was short then please present it. Presenting new, unsourced claims about putative defects of some theories is not adequate. --Michael C. Price ^talk 18:58, 22 October 2006 (UTC)

You're right, it's not BGV's argument. It's an older argument regarding bubble inflation. --ScienceApologist 01:16, 23 October 2006 (UTC)

I await your source(s) (preferably from the arxiv) that demonstrate that the expected past inflation is short.--Michael C. Price ^talk 01:24, 23 October 2006 (UTC)

E.g. [6], [7], [8] --ScienceApologist 01:47, 23 October 2006 (UTC)

No, you are failing to grasp the point I made earlier to Joke[9] that the unconditional expected duration of inflation (which is what those studies are calculating) and the expected duration of inflation, conditional upon our later existence are entirely different quantities. --Michael C. Price ^talk 03:13, 23 October 2006 (UTC)

If it's really that simple then we just need to reword the article to state that most cosmologists when they talk about the timescales of inflation are talking about the decay of the inflaton. Since there is no consensus on whether the pre-inflationary state was eternal inflation, pre-Big Bang, ekpyrotic, etc, we cannot make any statement about what the formation time-scale is (limits of cosmogony). How about that? --ScienceApologist 12:20, 23 October 2006 (UTC)

Fine, but we should mention that the two timescales are unrelated -- I don't want to have to go through all this again oneday. --Michael C. Price ^talk 14:47, 23 October 2006 (UTC)

I'm copying this text down here since I don't want to paste my response in the middle of all the stuff above:

It illustrates is that you and Joke do not have a good grasp of chaotic eternal inflation, since you claimed it violates the 2nd Law and Joke claimed it to be in conflict with "simple" dimensional analysis. --Michael C. Price ^talk 13:28, 22 October 2006 (UTC)

Frankly, I think you ought to keep your opinions about what I do and do not understand to yourself. This is particularly so because I never said that eternal inflation is in conflict with dimensional analysis: you put the words in my mouth.

The dimensional argument is perfectly simple to understand. The timescale for singularities to form is comparable to a Hubble time, simply because there are no other appropriate timescales in the problem (other than the Planck time, which is even shorter). I never suggested this doesn't mean it can't be 1,000 Hubble times, but it is hard to see how it would be 10³³ Hubble times. I find this argument difficult to understand:

I also note that neither of you have responded to the argument that the Bayesian-expected length of past inflation is unbounded or infinite: call the moment when eternal/chaotic inflation kicks off t=0. What is the expected value of t (i.e. the period of past inflation) for a typical observer? t is larger than any finite value, since there is more(*) "volume" (inflating and thermalised) to the future than to the past of any space-like hypersurface. (*"More" because there is only a finite volume to the past but an unbounded, infinite volume to the future.) Ergo the expected duration of past eternal inflation is infinite -- or at least very, very large, probably unbounded and certainly not "short".

Certainly if you fix an inflating surface at t=0 and look at some wordlines, they will all stop inflating fairly quickly in the future and, because of the BGV argument, in the past as well. Linde agrees that any given worldline ends in the past. He argues that their length could be unbounded, not infinite, so possibly the expectation could be infinite. Considering he has not provided an argument for this, or written a paper about it, it is safe, I think, to say that this is a view that can be left out of the article for now. My own guess, not that it is notable, is that at best, for infinite universes, it would be unbounded with finite expectation.

I think you are confused about how your statistical argument works. If you look at the surface defining the end of inflation in such a situation (under the volume measure) then the expected duration of inflation for any observer on such a surface is infinite, because the volume expansion during eternal inflation overwhelms the fact that only an infinitesimally small fraction of geodesics continue inflating beyond a certain point. This is the "observer-weighted" calculation. Unfortunately, this calculation doesn't make much sense. Assuming inflation ends with a timescale λ, the first calculation gives for an expected time:

$\int d\tau {\frac {\tau }{\lambda }}e^{-\tau /\lambda }=\lambda$

whereas the second calculation gives the nonsensical answer:

${\frac {\int d\tau {\frac {\tau }{\lambda }}e^{3H\tau }e^{-\tau /\lambda }}{\int d\tau e^{3H\tau }e^{-\tau /\lambda }}},$

where, since $3H>\lambda ^{-1}$ neither integral converges. There is some sense in which this calculation gives a "morally infinite" answer, and I think this is what you mean by "...conditional upon our later existence" above, because the expected duration of inflation does seem infinite in this case. However, this "observer-weighting" does not make much sense, and is still an open topic of debate in say, the string theory landscape (see, e.g. the recent papers of Vilenkin).

Finally, I think I should comment on the Aguirre-Gratton construction. You don't seem to have grasped that they have imposed very special boundary condition on a null hypersurface in de Sitter space. (It can also be implemented as, instead of an initial condition, imposing a symmetry under a certain reflection to form a kind of projective quotient of de Sitter space.) This can be thought of as imposing an "initial condition" (although it is not an initial condition in the usual sense, as it only provides partial information and cannot be used to evolve forward in time) on a surface from which time flows outwards. While this is a very interesting proposal, it is certainly not the generic case nor is it thought of as part of standard inflationary theory. –Joke 15:10, 23 October 2006 (UTC)

You say I should keep my opinions about what you understand to myself, but you are very free about speculating -- incorrectly as it happens -- about what I may or may not have grasped. Hypocrisy noted.

Sticking to the science I see you have repeated your dimensional claim and (again) ignored the fact that this has no bearing on whether the past inflation can have infinite duration. In the infinite case, of course, we should hardly be surprised that calculations yield divergent integrals.

Finally, the symmetry / initial conditions imposed in the Aguirre-Gratton are not mandatory, as they themselves note. What is important is that they demonstrate that the apparent presence of BGV proper-past-time-incomplete-geodesics is not fatal to models of past eternal inflation, which can be made singularity free. --Michael C. Price ^talk 16:57, 23 October 2006 (UTC)

1. You have not clarified your statement.
2. Do you agree that, per BGV and even Linde, that a past directed geodesic must end? The calculation I did, incidentally, was for future eternal inflation. In this case, you still have not clarified what exactly you are trying to say, despite tossing terms such as "Bayesian" and "conditional" around. I showed you one calculation in which the duration of inflation is short, and another in which it is impossible to define any sensible measure. Do you mean either of these, or something else entirely?
3. No, the boundary conditions they impose are mandatory. Otherwise it would violate the BGV theorem. The antipodal identification, however, is optional. –Joke 18:04, 23 October 2006 (UTC)
   1. I'm surprised you highlight the use of "Bayesian" since you introduced the term as "Bayesian proability" (sic). I used Bayesian to indicate that "expect" is to be interpreted statistically (as Expected value). I'll explain my use of "conditional" in my response to ScienceApologist below.
   2. To repeat: Aguirre-Gratton avoid BGV incompleteness by the manifold extension of region II (in a similar fashion to the Penrose diagram for the Kerr metric for a rotating black hole). Linde's observations predate the Aguirre-Gratton construction. The boundary conditions are a completely separate issue and are to adhere to the PCP, which is not mandatory. --Michael C. Price ^talk 11:02, 24 October 2006 (UTC)

1. Thank you for courteously highlighting my typographical error. I am questioning your use of the term "Bayesian" since we are discussing the length of worldlines in inflation, and you have not specified what prior distribution you expect to use to identify the length of inflating worldlines. It matters greatly which you choose, as I have emphasized above, and some weightings give you absurd answers.
2. Linde's observations are from a 2005 review. The Aguirre-Gratton proposals are from 2002 and 2003.
3. As for the manifold extension, if that were all there was to the argument then it would be trivial. It has been known that the flat slicing of de Sitter space is not geodesically complete for ages. The fact of the matter is that while the completion of de Sitter space has long been known, it does not work for de Sitter space plus matter because of the singularity theorems. See, e.g. Raphael Bousso, "Adventures in de Sitter space", hep-th/0205177 p.7. Any perturbations in the contracting region blueshift as the de Sitter throat is approached and cause a singularity to form. The novelty of the Gratton-Aguirre argument is that by specifying the special conditions hold on the null hypersurface corresponding to de Sitter throat (reversal from contraction to expansion) they reverse the arrow of time in one of the other regions. While this does circumvent the BGV argument, it is a special initial condition (or boundary condition – whatever) in just the same sense as the Hartle-Hawking no-boundary proposal.–Joke 16:47, 24 October 2006 (UTC)
   1. These incomplete geodesics may not be a problem in a fully quantised theory, just as we might expect the incomplete geodesics associated with classical black holes to vanish with their quantum evaporation. Who knows? No one. We are losing our focus here. It is clear that past eternal models have been published with infinite coordinate past time inflationary durations. Dismissing that as "physically irrelevant" is itself irrelevant orginal research. We are only concerned with veriable, reputable sources. --Michael C. Price ^talk 00:09, 25 October 2006 (UTC)
   • Observing that the fact that a model is past eternal in coordinate time is physically irrelevant is not original research: you can make anything past eternal in coordinate time with the correct transformations and this is obvious from any introductory book on GR. What is more important is that in the flat slicing of de Sitter space, the comoving geodesics (and only the comoving geodesics) are past eternal. The fact that the model is geodesically incomplete is a big problem. Read Hawking and Ellis's description of why they only consider geodesically complete manifolds in their book to see why. The fact that inflating models are geodesically incomplete has been recognized as a problem by most of the big players in inflation (other than Linde). Off the top of my head, I've seen comments from Guth, Vilenkin, Steinhardt, Albrecht, Hawking and Turok to this effect. I don't know what Mukhanov or Starobinsky have to say about it, but I would guess that Mukhanov's refutation of Starobinsky's model of primordial inflation from loop corrections to gravity must have been closely related. That seems significant, notable, and not to be original research. –Joke 04:57, 25 October 2006 (UTC)

You are confusing two different issues: the relevance of infinite past comoving time and the relevance of past proper time incomplete geodesics. The historical period of past inflation is linked to the former, not the latter. --Michael C. Price ^talk 07:28, 25 October 2006 (UTC)

See below. –Joke 16:07, 25 October 2006 (UTC)

I think what Michael is trying to say is that because there are some scenarios where one can get a past lightcone in a de Sitter-like space that ends at t = -infinity, that we need to make sure that we indicate there is no agreed-upon formation timescale for inflation. However, the inflaton mass/Hubble constant does set a decay time-scale for the duration of inflation once the inflaton is poofed into being (by whatever means you choose). I do think that BVG is a strong argument that places bounds on how inflation can occur. I think it is okay to discuss this in the article. I also think that BVG isn't directly refuted by the papers that Michael presents, but this is not the place to argue about such opinions. It is clear that the papers themselves present de Sitter spaces that have infinite past worldlines (even if those worldlines are very unlikely). --ScienceApologist 18:26, 23 October 2006 (UTC)

Thanks for encapsulating my argument in your first sentence: yes my point is that the inflation filled past light cone stretches back to t = -infinity, as clearly demonstrated in the Aguirre-Gratton geometry, but also true for all past eternal inflationary models. My particular take on BGV incompleteness is that it is physically irrelevant, so I am really not bothered to what extent the Aguirre-Gratton papers circumvent the BGV objection to past eternal inflation (although I do think they circumvent BGV successfully). In terms of what Wikipedia can say about BGV however, clearly Aguirre-Gratton regard their circumvention of BGV as sound.

Finally when saying that "infinite past worldlines are unlikely" we need to be careful about distinguishing a priori and conditional probabilities. As t tends to +infinity the fraction of inflating space vanishes, but the entire past light cone, back to t = -infinity, of the apex of every thermalised future light cone (one of which contains us) will be an inflationary de Sitter space. --Michael C. Price ^talk 11:02, 24 October 2006 (UTC)

I pretty much agree with SA here, except for the last and possibly first sentences (what do you mean by "formation timescale"?). The BGV argument is certainly very physically relevant as it shows that almost all past directed geodesics exist for only finite proper time (or affine parameter, in the case of null geodesics). The fact that it goes back to coordinate time t=-infinity is physically irrelevant. There is no such thing as an "a priori" probability in this situation and there are no agreed upon ways in which a sensible conditional probability can be computed. See Tegmark's paper ("What does inflation really predict?" for a discussion). –Joke 16:47, 24 October 2006 (UTC)

"Formation timescale" is a made-up term I coined in order to explain the differences between what you and I (and nearly everybody else who discuss inflation timescales) think is inflation timescale and what Michael is discussing (which is not the inflation timescale but rather is a speculation as to how we had a de Sitter space inflating in the first place). Your statement about coordinate time and physical time being different is definitely relevant here, but I have to admit confusion. My understanding of conformal diagrams is that coordinate times always represents physical times in the appropriate reference frames, though they may not necessarily represent the physical time of the worldlines being modeled. Am I mistaken? --ScienceApologist 18:25, 24 October 2006 (UTC)

I see. Well, in this case there are really two kinds of geodesics. For the comoving geodesics, the time coordinate t is the proper time along the worldline. Every other geodesics asymptotes to a null geodesic as t→−infinity and reaches the boundary of the conformal diagram in finite time. (See also comments above.) –Joke 04:57, 25 October 2006 (UTC)

Finite proper time, infinite conventional time for the non-comoving geoedesics.--Michael C. Price ^talk 07:20, 25 October 2006 (UTC)

If the proper time is finite then that means that the only people who perceive inflation to be infinite are those who aren't going through it, right? If this is the case then we have "eternity" that no one can directly experience, though people can observe. Similar to the observations made in the direction of event horizons, right? I'm now more convinced that Joke and I were right, there are no worldlines which extend to infinity in their own reference frame and therefore inflation did not have an infinite duration -- even if you want to have chaotic eternal inflation. --ScienceApologist 12:09, 25 October 2006 (UTC)

The proper time and conventional time are the same, and of infinite past duration, for the comoving geodesics/worldlines. These define the reference frame which we would normally measure conventional time by. So if someone asks what was the duration of historical inflation in the A-G model the answer would be infinity, unless you were using language in a seriously non-standard way. That the past time would be finite, as measured by an observer asymptoting in from the past null hypersurface, is not really relevant to the question, although it is very interesting. --Michael C. Price ^talk 13:19, 25 October 2006 (UTC)

The A-G model is not really at issue here. As I've mentioned, there is a special time in the past where expansion reverses to contraction and the arrow of time reverses. This circumvents the BGV theorem and is a fully consistent model with an unusual initial condition. But saying "these define the reference frame which we would normally measure conventional time by" is seriously problematic. Consider these points:

1. Proper time is what we normally mean when we say time. An observer wearing a wristwatch is measuring proper time: there is nothing at all "non-standard" about that. Almost all (all except a set of measure zero) geodesics terminate after finite proper time.
2. de Sitter space is SO(4,1) invariant. Inflationary spacetimes have this as an approximate local symmetry. The set of comoving observers is not invariant under this group (so a redefinition of your coordinates changes which observers experience inflation for an infinite proper time). This is because a SO(4,1) transformation changes which part of the full de Sitter space your inflationary spacetime covers.
3. A comoving reference frame is not uniquely defined in an eternally inflating universe (unlike a universe without large quantum fluctuations, where you can define one based on the value of the inflaton field). The "comoving observer proper time" is a physically unmeasurable quantity (only proper time differences can be measured) that barely makes sense to even talk about (for more on this see the Tegmark paper, "What does inflation really predict?").
4. The Cauchy problem is ill-defined for geodesically incomplete but extendible manifolds: you have to specify data on the parts of the manifold you have excised to solve the Cauchy problem. This is what Aguirre-Gratton have done.
5. Experts such as Guth, Vilenkin, Steinhardt, Albrecht, Hawking and Turok have clearly stated that it is a problem. The only person who seems to disagree is Linde, in a couple of short comments in a paper or two of his. –Joke 16:07, 25 October 2006 (UTC)

You're right, the A-G model is not really at issue here. That's all we really need to know, since the titles of their two papers are sufficient to indicate that they propose an infinite or unbounded period of past inflation; all else is original research. --Michael C. Price ^talk 23:47, 1 November 2006 (UTC)

That is completely absurd. It is not OR to actually read a paper and state what it says. The five points I've made above are easily found in the literature. They do not propose an infinite period of past inflation (simply because the universe is contracting sufficiently far in the past, so it would be "deflation"). What changes do you propose to make to the article? –Joke 02:28, 2 November 2006 (UTC)

The five points you made were irrelevant, just as it would be absurd to claim that the world was made "yesterday" by a logarithmic adjustment of the time coordinate. It is not absurd to state that some eternal inflation models are past eternal. What do you think "steady state" means? --Michael C. Price ^talk 05:57, 2 November 2006 (UTC)

That inflation represents a new steady state is a minority opinion. Those who speak of the duration of inflation are discussing the length of the last inflationary epoch which is set by a timescale and the Hubble constant. Previous inflationary epochs make for many steady state formalisms of eternal inflation in a process of progressive false-vacuum decay. There are only a very few arguments that have been made that the last bout of inflation was the only eternally-lasting inflationary period. --ScienceApologist 12:20, 2 November 2006 (UTC)

All specific models of inflation are currently minority opinions; anyway this would not be a valid criterion for omission from Wikipedia -- not to mention the steady state aspect of some models would be unbalanced. The phrase "progressive false-vacuum decay", in the above context, is misleading for chaotic eternal inflation, since a typical worldline projected back into the inflationary epoch would encounter a variety of inflationary rates / Hubble factors /vacuum energy densities, only the most recent values showing any form of progressive decay.--Michael C. Price ^talk 14:38, 2 November 2006 (UTC)

While specific models are "minority", there is a general consensus that the universe went through an inflationary epoch (validated by WMAP) that had a timescale set by the Hubble parameter (validated by WMAP). If you wish to believe that the Hubble parameter diverged dramatically at inflation so as to allow for other weird timescales that would cause inflation to last longer, or if you wish to believe that there is no data for how many e-folds of inflation occured, you really are constrained by WMAP observations which indicate in the bald form that inflation occured at 10^-33 seconds. There are ways around it, but they are in the minority understanding as illustrated by standard texts on the matter. --ScienceApologist 15:48, 2 November 2006 (UTC)

I can't believe this is a serious objection; the WMAP data only indicates that inflation switched off at a time we designate as t = 10^-33 by convention; it says nothing about whether inflation goes back to t = -infinity or not. --Michael C. Price ^talk 16:14, 2 November 2006 (UTC)

What you hide in that "by convention" clause is the subject of this dispute. I am arguing that the very fact the convention exists is the statement about the duration of inflation. --ScienceApologist 16:49, 2 November 2006 (UTC)

No, the convention is a relic of pre-inflationary cosmological models and thinking, which had a simple power relationship between the scale factor and the age of the radiation-dominated universe: $t\propto a^{2}$. As I said, it says nothing about whether inflation goes back to $t=-\infty$ or not.

Actually, this is incorrect. Since inflation occurs well above the Planck scale, it is impossible for the energy density to reach the Planck density in the normal sense. Certainly eternal inflation proposes ways around this, but conventionally, the epoch is not just set by extrapolating back from the radiation dominated phase, it is also set by basic extrapolation of DeSitter spaces back to high densities. --ScienceApologist 13:08, 3 November 2006 (UTC)

By Planck scale I presume you mean Planck length scale, not energy scale? Even so the rest of your statement doesn't make much sense to me (what exactly is "incorrect" about my previous statement?), in that it seems irrelevant to the point we are discussing. As Joke has observed elsewhere, we seem to be perpetually talking past each other. --Michael C. Price ^talk 13:21, 3 November 2006 (UTC)

Sorry, I was talking about the size of the universe rather than the energy density. What was incorrect about your previous statement was the claim that the convention is purely a pre-inflationary relic. It isn't. --ScienceApologist 13:33, 3 November 2006 (UTC)

This is going nowhere. It's clear that the whole topic of past-eternal inflation needs it own subsection where the concepts, pros and cons can be clearly explained, rather than just alluded to in passing. I propose we split the eternal inflation section into future- and past-eternal inflation subsections. What say others? --Michael C. Price ^talk 14:57, 3 November 2006 (UTC)

Well, I actually think that this all ought to go into an article (not a redirect) called eternal inflation and we should write something pithy here. –Joke 15:04, 3 November 2006 (UTC)

Sounds sensible. BTW there is already a stub chaotic inflation. --Michael C. Price ^talk 15:11, 3 November 2006 (UTC)

This whole discussion of wether inflation is finite or infinite (and for which observer) is like the discussion between two ants on a tree, which debate the fact that although every branch they meet, has finite length, each branch can have off-spring, and therefore the tree (which they are unaware of) is potentially not ending but goes on indefinite. From our point of view though it is obvious the tree has a finite length, but then we are also aware that the tree grows. An naive perspective would then be that if you calculate back to the past, the tree must have started from zero length, which is quite impossible. Untill of course we discover that the tree started off as a seed, and that the seed was an offspring of a previous tree. And then we can ask, when was the first tree formed. All realistic models of tree evolution also goes back to some time in which the first tree must have been formed. Etc. So this discussion is never ending, and can be repeated at all levels of the material world. The (philosophical) important fact to consider is that both the finitude and the infinitude of the world (finitness of time and infinitness of time, for example), are equally absurd. The difficulty is of course that the infinite can not be grasped without contradictions, and in fact the infinite is full of contradictions. It is just because infinite is contradiction, that it is an infinite process, unfolding endlessly in time. See for example [Engels/antiduhring/Time and space http://www.marxists.org/archive/marx/works/1877/anti-duhring/ch03.htm] Heusdens 14:01, 10 January 2007 (UTC)

Eternal Inflation

Two refs on the subject of eternal inflation were moved -- one of the links was incorrect. I've corrected it and restored the links (which appear twice). They seem relevant to both sections. --Michael C. Price ^talk 06:09, 18 October 2006 (UTC)

I tried to split the difference and put the links at the start of the "initial condtions" section as a sort of entrée to the section. –Joke 04:36, 25 October 2006 (UTC)

Energy for Inflation

I have a question. Matter and anti-matter were created in nearly equal amounts by the big bang. They annihilated each other, and the tiny residual fraction of matter left is what we see as the universe today. When did that period of annihilation begin? Could the matter/anti-matter annihilation have provided the motive force behind inflation?--Drcruzr 03:46, 25 October 2006 (UTC)

No, because inflation empties the universe out – so any asymmetry created before inflation would quickly be diluted until there was less than one baryon (particle of matter) in the universe. The process you describe is called baryogenesis and must have happened after a period known as reheating in which inflation ends and all the inflationary energy is converted to particles. –Joke 04:35, 25 October 2006 (UTC)

A Catholic friendly version of inflation? Is it ruled out?

I gave this section that title because this article (http://en.wikipedia.org/wiki/Multiverse_%28science%29) states that Catholic Church rejects multiverses, so I guess that Catholic Church hates Andrei Linde, Alexander Vilenkin, Alan Guth, Sean Carroll, Max Tegmark, and Leonard Susskind's views on inflation.

I think it would be important to add some information about hybrid inflation here. According to Linde, the hybrid inflation models are not eternal (therefore, friendly to the Catholic Church), but I think it is ad hoc to add additional scalar fields, and the classical chaotic inflation seems to be the most simplest version of inflation.

http://arxiv.org/abs/astro-ph/0610074 http://arxiv.org/abs/astro-ph/0603539

So from reading this papers, how are hybrid inflation models affected by the cosmic microwave background radiation results? Does it support hybrid inflation or it rules it out? LinkinPark 19:46, 29 November 2006 (UTC)

I've amended the multiverse entry -- the claim of catholic hostility was not supported by the sources. --Michael C. Price ^talk 20:12, 29 November 2006 (UTC)

Any comments on hybrid inflation though, I am curious about it. If it is correct, it gives a huge break to the fine-tuners. If not and eternal inflation is correct, well, they lost a powerful argument. To me, it destroys the idea of a God that interferes in human affairs, but let's talk about hybrid inflation instead. LinkinPark 20:19, 29 November 2006 (UTC)

Regarding the Catholicism aspect: http://www.millerandlevine.com/km/evol/catholic/schonborn-NYTimes.html

Overview section edits

Hi, I did some more-or-less heavy rewriting on the "Overview" section, I thought I should explain why here. I think the paragraph I edited was going for an explanation of why the no-hair theorem works, and I've tried to keep in the same spirit. But as it was I think there were a few problems.

• For one, it lacked transition between talking about the problems inflation solved and why it solves them.
• Talking about matter dominated and radiation dominated universes is useful, but including a discussion of how the Hubble parameters change is a bit misleading -- the universe is neither matter nor radiation dominated during inflation, and the Hubble parameter is nearly constant. Also the explanation of why the radiation energy density falls more quickly might be better off somewhere else...
• The standard big bang theory doesn't say the universe is "mostly full of matter now." It actually doesn't much care what the universe is full of currently, but the consensus Lambda-CDM model says that the universe is currently dominated neither by matter nor radiation, but by a cosmological constant.
• Next things got a little confused. To clear things up, as mentioned the matter density goes like a^-3 and radiation like a^-4. Also inhomogeneities scale something like a^-2 when the universe is roughly isotropic, anisotropies (also fixed by inflation) go like a^-6, curvature (see Friedmann equations) goes like a^-2, and exotic particles go like matter -- a^-3. So the assertion that "The densities of matter and radiation actually fall faster than the densities of inhomogeneities, curvature and exotic particles..." isn't true.
• Also, during inflation there really isn't any matter or radiation. There could be, but one of the reasons for inflation is that it dilutes any stuff initially present into nothing. The matter and radiation in the present universe is created during reheating. So the reason that inflation smooths out the universe involves a comparison between the inflaton energy density and that in the undesirables.

I think that covers most of it. If anyone has any issues with this edit, please let me know. Wesino 00:37, 1 December 2006 (UTC)

I didn't see these edits until now. I think your edit is good. My only point is that the reason for mentioning the evolution of the Hubble parameter is to point out that the physical Hubble scale is changing rapidly in matter and radiation dominated universes, so that the physical conditions are changing rapidly. However, the Hubble parameter is roughly constant in inflation, which means that it corresponds to a much more symmetric state (technically, a nearly-stationary state). However, I think the text is fine without pointing this out as well. –Joke 22:07, 3 January 2007 (UTC)

an ongoing misconception with exponential expansion

It seems there's a subtle misconception regarding "exponential expansion" that pops up pretty consistently during the article. I think it's tied in with the different between old and new inflation, which isn't perhaps made as clear as it could be.

• The expansion is only truly exponential (eg, a(t) = e^Ht) in Guth's old inflation model. This is because the inflaton field is stationary, and thus it acts like a cosmological constant, driving de Sitter expansion.

• In new inflation, the expansion is not exponential. It is nearly exponential, in the sense that the Hubble parameter is roughly constant (ie (dH/dt)H^-2) is a small but nonzero number). The expansion is not exponential because the field is rolling, and its kinetic energy makes the pressure somewhat more than minus the energy density, so it doesn't act like a cosmological constant and spacetime isn't de Sitter.

The deviation from pure exponential expansion in new inflation is extremely important -- if the (new inflationary) expansion were exactly exponential, inflation would produce an exactly scale invariant spectrum. The fact that the inflation isn't quite exponential leads to the prediction that the primordial perturbation spectrum is nearly scale invariant but not exactly. Also, the idea of a rolling field is central to why new inflation works and old inflation doesn't, and so it's an important feature of the model.

So I'd suggest that in further edits we steer clear of calling expansion "exponential," unless we're talking about old inflation specifically -- then we should be clear to delineate it! A good recent reference for this is a paper by Paul Steinhardt and collaborators, one of the new inflation inventors [10]. Wesino 01:00, 1 December 2006 (UTC)

Yes, everything you say is correct. However, I think this is all in the article (see, for example, the observational status section). Of course calling it exponential is not an exact statement, but it is close enough that physicists call the expansion exponential all the time. In the slow-roll regime, the Hubble parameter is decreasing and the expansion more accurately resembles a power law. However, in the chaotic regime, where the dynamics of the inflaton are more accurately described by a Fokker-Planck equation and fluctuations up the potential are common calling it "exponential" is better motivated. In any case, feel free to put "nearly" in front of each exponential: I don't think that would reduce clarity, and it adds to accuracy. –Joke 22:00, 3 January 2007 (UTC)

A discussion on non-eternal inflation

I think this page needs a discussion on the viability of non-eternal inflationary models. LinkinPark 16:16, 5 December 2006 (UTC)

I will add some information about hybrid inflation back into the article from this old edit:

http://en.wikipedia.org/w/index.php?title=Cosmic_inflation&diff=50308877&oldid=50299760

"A set of models called hybrid inflation solves this problem by introducing (at least) one more scalar field (a second inflaton), so that one of the inflatons is responsible for most of the energy density (thus determining the rate of expansion), while the other is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton won't affect inflation termination, while fluctuations in the latter won't affect the rate of expansion. Therefor hybrid inflation is not eternal. When the second (slow-rolling) inflaton reaches at the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the this inflaton down its potential, leading to termination of inflation" —The preceding unsigned comment was added by LinkinPark (talk • contribs) 05:04, 11 January 2007 (UTC).

History and Origin of the idea of inflation

The theory about a regime of rapid expansion prior to the big bang did not start with the work of Alan Guth, just that the first theory with this idea which was named 'inflation', happened to be the theory of Guth. Prior to Alan Guth's idea there was the model of the early universe by the Soviet scientist Alexei Starobinsky at the L.D. Landau Institute of Theoretical Physics in Moscow, comparable to that of inflation. I think that the Wiki page on cosmic inflation should give credit to the fact that Starobinsky was the first scientist to have come up with such a radical concept, even though it has been said that Alan Guth developed his model of inflation some years later independend of the work of Starobinsky. Remarkable also is the fact that already before such ideas have been proposed, as for instance by Fred Hoyle, who envisioned that in the Steady State universe, matter would be continually created by a process very much like inflation, so that the Steady State universe, although continually expanding, would still remain static because new galaxies could form from hydrogen and other light elements produced in this process. So the least this explains that the idea of inflation by Alan Guth was not original, although the idea became increasingly popular due to the publication of this idea in a paper by Alan Guth.

See also this excerpt from David Griffin ("Inflation for beginners")

[ redacted copyvio Joke 17:30, 10 January 2007 (UTC) ]

Heusdens 16:56, 8 January 2007 (UTC)

You might have notice that Starobinsky's work, along with the early work of Mukhanov and others in the Soviet Union, is already prominently mentioned in the history section. It is generally acknowledged that while Starobinsky's work was the most significant precursor to inflation, he didn't have quite the same things in mind as Guth. Namely, Starobinsky didn't discuss the solution of the classical cosmological problems: the flatness, horizon and monopole problems.

Gribbin's discussion of Hoyle's steady state universe seems highly idiosyncratic to me and is certainly not the mainstream viewpoint. In fact, I've never heard it mentioned before. For example, the inflaton has no significant creation of ordinary matter during the inflationary epoch (only quantum fluctuations in the inflaton), unlike the steady-state cosmology. Moreover, a key part of inflation is that it ends (even though inflation is generically future eternal, along any worldline inflation must eventually ends and the universe must reheat), whereas the "steady-state" scenario is supposed to be eternal. –Joke 17:30, 10 January 2007 (UTC)

De-merger/resurrection proposal

I see that inflationary epoch was merged into cosmic inflation a little while back, and is now just a redirect. I would like to propose resurrecting a brief inflationary epoch article. It is listed as an epoch of the early universe in Graphical timeline of the Big Bang, but anyone following that link to this very detailed cosmic inflation article would have to look long and hard to find answers to basic questions such as "when did it begin", "when did it end", "what happened between those times" etc. I think resurrecting a short summary article with the basic facts and a link to cosmic inflation for more details would be helpful. I am happy to do the job, but I just wanted to check that there aren't any big objections first. Gandalf61 16:09, 8 February 2007 (UTC)

Sounds good to me, I was here recently looking for that information. When did it stop and why, and couldn't find it. LilDice 16:33, 8 February 2007 (UTC)

No objections, so I've gone ahead and resurrected inflationary epoch. Gandalf61 17:53, 10 February 2007 (UTC)

Revert to revision 124898742 dated 2007-04-22 17:02:49 by Pizza1512

I did the revert because the addition of "atheist" to describe Guth, Linde, Steinhardt and Albrect was not supported by any verifiable, reliable sources. Also the religious beliefs of these people are completely irrelevant to the article. The proper place for such assertions -- properly referenced -- would be in a biography of the relevant scientists. Wesino 07:28, 25 April 2007 (UTC)

String inflation

Could someone expand the string inflation section(s) a bit? I see from New Scientist that string inflation predicts we will not detect gravity waves in the CMB. But if string inflation takes place at a very high energies (quantum gravity energies?) it presumably cannot explain the absence of magnetic monopoles, since the latter are widely hypothesized to be produced by GUT symmetry breaking (i.e. later, at a lower temperature, than the string inflation. Or is it??). The only solution would be to conjecture (as it has been) that inflation happens multiple times as the universe cools, with at least one phase after GUT symmetry breaking. But if this is the case then any gravity wave signature (or lack of) from the earlier phases would be lost, since inflation always wipes the astro-historical slate clean.

BTW here's the NS source Testing String Theory with CMB by Linde and Kallosh It implies that the mass of the gravitino places an upper bound on the Hubble constant during inflation. So the prediction is either no gravity waves or a superheavy gravitino (which is apparently a problem). --Michael C. Price ^talk 12:57, 20 July 2007 (UTC)

superinflation

What is superinflation and how is it linked to this article? 82.18.22.160 (talk) 12:31, 22 December 2007 (UTC)

I suppose you're talking about super-exponential inflation--it is expansion at faster rates than de Sitter expansion. Here's an on-line review and a link to the pdf-

http://arxiv.org/abs/gr-qc/9809071 Mytg8 (talk) 17:52, 4 June 2008 (UTC)

Theory

Am I one of the few who believe this theory to be almost ignorant?

Cosmic Inflation is based on observations of the observable universe. From what I understand in order to correctly state that an object is increasing in size, you must first be able to determine that object's size and verify that it is increasing. For example: When you fill a latex balloon with air, the latex of the balloon is expanding. This is observable since an observer is able to see the entire balloon. Is it not fair to say that if the latex of the balloon moved outward in every direction then it has expanded.

By the same token: If you observe an expanding portion of an object, it is completely possible for the entirety of the object to remain the same size. If all parts of a living cell move toward the cell wall in every direction, it does not mean the cell is expanding. It simply means that the parts of the cell are closer to the cell wall.

This brings me to several issues:

• If the universe is indeed expanding, what is where the universe is not? Even if it is empty space, it is still space; filled or not, it is still part of the universe. The observable part of the universe may be expanding from our POV, but the universe is both filled and empty space. Unless it is part of a larger body and actually ends at some point, it will stretch on for infinity.
• If you were inside a sphere that was expanding, but you knew there was space (empty or not is irrelevant) outside of the sphere, would you be correct to say that the sphere AND the space around it were expanding?
• Are scientists ironically assuming that our observable universe is at the center of the universe? In history its happened before, so why not learn from our mistakes. Not that I personally doubt the Big Bang Theory, but I'm sorry, existence is a pretty imaginably large space... to assume we are in the center (or near enough to the center to able to observe expansion) is absurd.

Anyone... please address any or all of these issues, I really cannot type all of the issues that I run across in my mind, because I am very scatter-brained. I'm not trying to start an argument I want opinions, I want to be proven wrong or right and LEARN. Robert M Johnson (talk) 11:05, 16 January 2008 (UTC)

We have an article on the metric expansion of space. You could start by reading this article carefully, then reading the articles that it links to (such as metric (mathematics) and Riemannian geometry) to fill in the parts that are not clear to you. To briefly answer some of your questions:

• The universe is not expanding into anything - indeed there can be, by definition, nothing outside of the universe for it to epxand into. The metric expansion of space is an intrinsic expansion.
• Theories of modern cosmology do not assume that we are at the "centre" of the universe. Rather the opposite - they assume that the universe is homogenous and isiotropic. In other words, the large scale features of the universe are the same no matter where you are or which direction you look in. This Cosmological Principle says that there are no special places in the universe. Gandalf61 (talk) 12:43, 16 January 2008 (UTC)

First, let me say Thank you for your help. I understand the metric expansion of space, and was never taught this before, however I'm having difficulty comprehending how the Copernican principle (which is ironically something I listed, unnamed, above) makes the universe homogeneous and isotropic and how those two comprise the theories of cosmology. I need it explained using many synonyms and having many words defined so that I may understand. (its sort of hard jsut to jump into all of this terminology, uneducated) Basically explain, if you would, the fact that earth is no place special because there are no special places in the universe, and explain why there are no special places in the universe. 71.239.147.154 (talk) 13:22, 16 January 2008 (UTC)

The discussion page of a WP article is not the place to go to learn how things work. That's what the article pages themselves are for. That's what school and books are for. The discussion pages are for discussing what should be in the article and how the information should best be presented. Asking for "many synonyms and having many words defined" is a fair request to make of a professor, but not part of making this a better article. If you think something in the article needs to be better explained, then by all means raise your concerns and offer suggestions here. But don't come to a discussion page, say that you think the theory itself is "almost ignorant," and then list the reasons why you don't understand it with the expectation of being educated here. Please understand the difference between "I don't fully understand the basis for this theory" and "I think this theory is almost ignorant." Dcs002 (talk) 22:18, 30 October 2009 (UTC)

On the separation of observers

I think the best way to get at this idea is to expand the de Sitter metric in local coordinates around a geodesic, but I could be wrong.Likebox (talk) 18:25, 19 April 2008 (UTC)

I have restored the text:

Expressed in comoving Cartesian coordinates the proper distance is:

$ds^{2}=-c^{2}dt^{2}+e^{2Ht}(dx^{2}+dy^{2}+dz^{2})$

where H is the Hubble scale factor induced by the inflation. Inflation corresponds to the appearance of the $e^{2Ht}$ term in the above expression.

I see no valid reason for its removal. Please do not remove without discussion first.--Michael C. Price ^talk 19:55, 19 April 2008 (UTC)

Sorry--- the reason I removed it is because the quantities "dx dy and dz" mean different things than in the expression for the metric a little later. They are a different coordinate system. In this case that you added, they are geodesic quantities which follow particles along geodesics. In the stationary polar metric, they are coordinate differentials in one causal patch and only can follow one geodesic. These are two completely different physical points of view. One is the point of view of global space-time, the other is the point of view of a single observer.

Although in the original writing, the two points of view are kept separate, now the points of view are mixed together. I think it would be better to move the stuff to a later position, and I didn't want to just delete. I tried to rewrite at the end of the section what the system looks like in global geodesic coordinates, but I couldn't find a good text before you restored. I didn't mean to suggest that the material is inappropriate, just awkwardly placed.Likebox (talk) 20:01, 19 April 2008 (UTC)

Oh--- and the horizon form of de Sitter space is the preferred way that string theorists like to do it, because it is more in spirit with the holographic principle. It's not OR, just a different community's take on things.Likebox (talk) 20:05, 19 April 2008 (UTC)

I withdraw the OR point then! But "dx dy and dz" are not used later. In the polar expression it is r etc. I really think that before we start using polars we should explain the more straight forward cartesian position. I agree they are completely different viewpoints -- but that is why I think they should be explained together. Otherwise the casual reader will think they are contradictory.--Michael C. Price ^talk 20:10, 19 April 2008 (UTC)

I think you might be right--- sorry for being hasty.Likebox (talk) 21:11, 19 April 2008 (UTC)

Name change?

I suggest we rename this page Inflation (physics). All scientific publications, popular and more serious, (see the current issue of New Scientist for example) just call it inflation, never cosmic inflation, which just sounds so amateurish.--Michael C. Price ^talk 06:32, 6 June 2008 (UTC)

I think some people call it Cosmological Inflation, which sounds less dopey.Likebox (talk) 06:40, 11 June 2008 (UTC)

Yeah, that doesn't sound quite so bad. Perhaps we should have a vote? --Michael C. Price ^talk 08:36, 11 June 2008 (UTC)

I agree -- Inflation (physics) sounds more reasonable. SwordSmurf (talk) 12:38, 11 June 2008 (UTC)

There's a discussion potentially relevant to this going on at (oddly enough) inflation (financial) (which used to be at inflation and may be again one day, although it probably should be at inflation (economics)). Specifically, it would be good if people who agree that we always just call it "inflation" could weigh in over there, especially if they agree with me that the page at inflation should be a disambiguation page (or maybe even this article, but that's probably too much to ask) instead of the economics article. Currently there are several regulars who think they have a consensus that our inflation is insignificant. False vacuum (talk) 05:00, 29 March 2009 (UTC)

In fact, the page has been moved already (back to inflation), even though the discussion is still going on as far as I can tell. Nevertheless, if I can get some support, perhaps we can move it again. False vacuum (talk) 05:39, 29 March 2009 (UTC)

I think "inflation (cosmology)" would be superior to "inflation (physics)". Especially considering that people might confuse "cosmic inflation" with the physics of inflation in general (aka blowing into balloons). I don't particularly care about cosmic inflation vs. inflation (cosmology) however.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 06:12, 29 March 2009 (UTC)

I guess it is conceivable that inflation (physics) could refer to balloons, so I guess that inflation (cosmology) is superior. There seems to be a general consensus here that we should make the move, and certainly no need to wait for the folks at inflation (economics) to make their minds up. Any objections? --Michael C. Price ^talk 07:22, 29 March 2009 (UTC)

We seem to have a number of choices:

1. inflation (astronomy)
2. inflation (cosmology)
3. inflation (physics)

Any others? --Michael C. Price ^talk 08:02, 29 March 2009 (UTC)

• I'll put in my vote for Inflation (cosmology). This clearly denotes the right context for the subject, it clearly sides steps the issue of whether this is physics or astronomy (simply because cosmology shares this ambiguity). Moreover, inflation (physics) could be thought to refer to something else involving air. (TimothyRias (talk) 08:58, 30 March 2009 (UTC))

Okay, I tried to move it to Inflation (cosmology) but the existing redirect seems to block it, so it's becomes Inflation (astrophysics), as a temporary measure. I've left a request to get this fixed. --Michael C. Price ^talk 09:48, 30 March 2009 (UTC)

East Vs. West

I hope that the physics wiki can stay neutral in the east/west business. A lot of this work was done twice, but I don't know the history of this field at all.Likebox (talk) 03:16, 19 June 2008 (UTC)

Comoving picture vs. One-Patch picture

I deleted the comoving picture--- but it certainly should be restored in its own section. The problem I had with the current wording is that it says "the distance is given by", when talking about the metric, which does not immediately give the distance between observers, but only the distance between infinitesimally separated points in a system of coordinates. To find the exponential separation of observers from the metric you should really be following geodesics (but in this case the difference is pretty trivial because the space-time is homogenous). Using the one-patch metric, homogeneity plus the properties of the horizon allow you to immediately see what the geodesics do without any work.Likebox (talk) 19:29, 23 September 2008 (UTC)

what the variables mean

In the Space expands section there is a formula where the definition of the variables is not given. I think the formula should be followed with something along the lines of: where t denotes time, $\Lambda$ denotes.... jbolden1517^Talk 16:00, 13 December 2008 (UTC)

A question, but not planning on editing anything so dont slam.

If space itself is expanding faster than the speed of light, then doesn't that mean that information would be unable to cross space to effect opposite ends? Even if the space was small enough before inflation began, there would still be areas that were uneffected by information after inflation because any info that happens during inflation cant possibly reach the edges of the universe.--GundamMerc (talk) 02:50, 17 February 2009 (UTC)

This comes up when people discuss the remarkable uniformity of the cosmic microwave background. Discussion of this sort is really better suited to Wikipedia:Reference_desk/Science, though. - Eldereft (cont.) 03:45, 17 February 2009 (UTC)

Thank you for telling me about reference_desk.--GundamMerc (talk) 13:53, 17 February 2009 (UTC)

Have a look at Horizon problem. --Michael C. Price ^talk 15:56, 17 February 2009 (UTC)

How can you tell the difference between a homogeneous universe and just detecting the same energy in all directions? Its like being in a fog, you can't tell whether it is just in your local area or if it stretches across the world, but it looks the same either way.--GundamMerc (talk) 12:44, 20 February 2009 (UTC)

The fog is "thin" enough that you can see a long way through it, right to the edge of the observable universe, but "thick" enough that you can detect it as well.--Michael C. Price ^talk 12:57, 20 February 2009 (UTC)

Disambiguation

Does anyone other than User:Lawrencekhoo feel that there needs to be a disambiguation hatnote or a direct link to Inflation (the economics article) at the top of this one? False vacuum (talk) 22:31, 30 March 2009 (UTC)

No objections to losing the sentence For a general rise in the level of prices, see Inflation. since we still have the dab pointer. --Michael C. Price ^talk 22:49, 30 March 2009 (UTC)

I've taken out the direct link to the economics article, and added something else. See also inflation (disambiguation) (if it hasn't already been reverted). False vacuum (talk) 23:46, 30 March 2009 (UTC)

Since Inflation theory and Inflationary theory and various other inflation titles redirects here, its unreasonable to take out the diambig pointer to the most common use of the term inflation. LK (talk) 08:30, 31 March 2009 (UTC)

I don't see the need for repetition -- the pointer to inflation (disambiguation) is enough. On a separate although related issue, I don't think "inflation theory" etc should point to physical inflation. Like it or not, "inflation"'s most common usage is in the economic sense. --Michael C. Price ^talk 09:37, 31 March 2009 (UTC)

But are the terms "inflation theory" or "inflationary theory" commonly used in an economic sense? (This isn't a rhetorical question; I don't know the answer.) (I'll leave aside my concerns about the use of a popularity contest [as judged however anyone likes, really] to decide these sorts of things, at least for now. I'm tired of arguing and need to get some work done.) False vacuum (talk) 22:33, 1 April 2009 (UTC)

I take back what I said: the top goggle hits for both "inflation theory" are "inflationary theory" are for good o'Guth inflation. I'm staggered. Good news, though. --Michael C. Price ^talk 05:40, 2 April 2009 (UTC)

I'm also concerned about the lack of any link to the inflationary epoch article. I thought the dab. header was a good place for it, since "inflation" is frequently used (in the context of cosmology, which is the subject of the article) to refer to the inflationary epoch. I might add that the reason I was looking for this article the other day was precisely to find out when inflation started and ended—information which is in the inflationary epoch article and not this one. False vacuum (talk) 22:56, 1 April 2009 (UTC)

As long as the terms "inflation theory" and "inflationary theory" and various other redirects point here, I think the hat-note should include a link back to inflation. I really don't see the problem with including such a short note at the top of the page. Please note that the hat-note at Inflation includes a link back to this page, as well as the diambiguation page. LK (talk) 05:34, 2 April 2009 (UTC)

Since there are no objections, I have changed the hat-note. LK (talk) 14:45, 4 April 2009 (UTC)

There are in fact no wikipedia articles that link to Inflation theory or Inflationary theory intending anything other than cosmological inflation. This turns out to be surprisingly easy to check (and I've just made it still easier). The only reason I can think of why there needs to be a pointer to inflation (i.e. inflation (economics)) at the top of the page is if it's possible for someone to end up here while trying to get there. Am I missing anything? False vacuum (talk) 22:38, 4 April 2009 (UTC)

Well, I haven't thought of any new reasons not to remove that annoying sentence from the hatnote, and no-one else has suggested any, so out it goes again. Isn't this fun? False vacuum (talk) 20:51, 8 April 2009 (UTC)

Look, if you want to keep 'Inflationary theory' & 'Inflation theory' redirecting here, the hat note should stay. Its a plausible search term for inflation theory in economics. If you want to get rid of the hat note (I don't see the point) then redirect those pages (and other redirects) to the disambig page. This is not a 'keeping score' thing after all, its about making sure that people can easily get to the page they want. LK (talk) 15:40, 10 April 2009 (UTC)

East/West

I think that the Starobinski mechanism is almost identical to Guth's. The only difference was the mechanism. The detailed predictions were worked out by Mukhanov and collaborators a little later, in 1981. The "citation needed" is to establish that Guth indeed was first, or whether he was simultaneous with Starobinski (or even slightly later). It is pretty clear that they are independent discoveries, but it is important not to slight the Russians.Likebox (talk) 18:45, 8 April 2009 (UTC)

I should say that Starobinski's is almost identical to Linde et al, because it doesn't seem to suffer from any graceful exit problem. To get that far takes some ingenuity with a scalar inflaton.Likebox (talk) 20:49, 8 April 2009 (UTC)

I don't follow. The article says "At the same time, Alexei Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the universe with an exponentially expanding deSitter phase." quantum corrections to gravity doesn't sound like inflation at all, which is a consequence of negative pressure in (classical) GR. Nothing to do with QG. To be cruel, it sounds like Starobinski was hand-waving without any sort of mechanism. --Michael C. Price ^talk 07:55, 16 April 2009 (UTC)

You aren't being cruel, you just haven't read the paper. Quantum corrections to General Relativity means that you have additional terms in the Einstein equation corresponding to extra stress energy, R^2 terms. If you start with a universe with a high curvature, the extra terms produce an effective cosmological constant. Starobinski noted this, and then solved for the behavior of the universe assuming it started off with a cosmological constant by whatever mechanism you like.Likebox (talk) 23:42, 16 April 2009 (UTC)

It's true, I haven't read the paper. Is it on-line? Was he predicting open-ended exponential growth? --Michael C. Price ^talk 09:08, 17 April 2009 (UTC)

The one in Physics Letters paper cited is the one I read, it's available online, but maybe not without subscription. I am not 100% sure about the precise end to the inflation in this mechanism, I don't much of an intuition for R^2 gravity. So I guess I was being a little glib in the answer above. My current thinking is that the main point is that if the curvature is small, you reduce to GR with zero or very small cosmological constant, but when the curvature is big, you have GR with a big cosmological constant. Presumably then there is a smooth interpolation solution, where the curvature slowly gets smaller, and as it unwinds, the spacetime slowly gets flat--- just like normal slow-roll scalar inflation.

This picture has some sweet properties--- the "inflaton" is really just a part of the gravity field, so the analog of the inflaton potential is not arbitrary. It's determined by the one-loop corrections, and these are definite once you have an effective low-energy quantum gravity field theory model which has definite one-loop coefficients. You can find the one-loop coefficients in string theory, but I don't think that the one-loop corrections depend much on the precise details of high energy quantum gravity. According to a talk by Mukhanov which I saw recently (that was the motivation for the edits), the perturbations which are predicted by this model, the deviation from scale free gaussian spectrum, are consistent with other slow-roll models. He also says that the Workshop book makes some mistakes in the spectrum of the perturbations by oversimplifying--- it leaves out what he calls the spectral index, the deviations of the perturbations from a pure scale free spectrum. Mukhanov's prediction for the deviations from scale free spectrum is a .02-.08 in the exponent, but again, I didn't read his technical papers. He has a book, but it isn't free. I don't know enough to say any more. Wish I did.Likebox (talk) 15:06, 17 April 2009 (UTC)

Thanks. I see that Starobinski's letter has become one of the "most cited" on gr-qc archives. Probably worth while having a separate section in the inflation article.

Looking at just the abstract, I get the impression that Guth and Starobinski were coming at the problem from different ends. Guth was invoking inflation to explain how a tiny chaotic universe can grow, in the post quantum gravity era, into an enormous isotropic universe without monopoles. Starobinski, conversely, was using inflation to explain how a tiny isotropic universe could be created, in quantum gravity era without an initial big-bang singularity. Presumably Starobinski-inflation ends when the quantum gravity era terminates? Different mechanisms, different cosmological eras, but same inflationary process. --Michael C. Price ^talk 20:36, 17 April 2009 (UTC)

I agree. On a side note, I find these American/Soviet synchronicities fascinating, especially now that the cold war is fading into the mists of history.Likebox (talk) 21:26, 17 April 2009 (UTC)

Definitely. Like the frozen star / black hole picture. --Michael C. Price ^talk 22:58, 17 April 2009 (UTC)

That, and there are more examples: The Higgs mechanism was also discovered in the early 1960s by Polyakov and Migdal (it's in a Polyakov interview) but they couldn't get their paper published! Landau's criticism of quantum field theory based on the Landau pole "zero interaction phenomenon" was too dominant. Wilson/Polyakov developed Lattice gauge theory, 'tHooft and Polyakov found Monopoles. Kolmogorov/Onsager/Heisenberg developed statistical turbulence theories in the early 1940s when the division was Communist/Capitalist/Fascist. Pomeranchuk-Gribov/Chew-Frautschi developed similar S-matrix ideas. I think that the Soviets were generally more up on the western literature than the westerners were up on the Soviet literature, so the Russians are slightly ahead (in cases where they were slightly behind, the paper would not have passed peer review). Maybe there's some cribbing going on in some of the examples, but certainly not for inflation. This double-checking by two mostly independent collectives on opposite sides of the iron curtain I think was helpful to the progress of science, although I'm sure it wasn't a boatload of fun for those involved.Likebox (talk) 16:34, 18 April 2009 (UTC)

Philosophy of Inflation

This section has a paper by Earman and Mosterin which combines flawed (but understandable--- they aren't cosmologists) misunderstandings about the details of inflation with a valid philosophical point. The point they are making is that the transition from FRW to inflation is motivated entirely by the desire to remove one sort of fine-tuning, the fine-tuning of initial conditions, and to replace it by another sort of fine tuning, the fine tuning of the cosmological constant at the end of inflation, and of the parameters of the inflaton potential.

Nearly all cosmologists accept that the latter sort of model is vastly preferable, since the fine tuning of the cosmological constant is required for other reasons already, and the potential fine tuning is an open condition, it selects a region of parameters which is not special in any way. In contrast, the fine tuning required to make a cosmological model which does not involve inflation requires adjusting the initial temperatures and curvatures of causally disconnected regions to match very precisely, but not quite exactly. It is obvious that that kind of fine tuning is much, much worse. But this type of criterion, comparing different types of fine-tuning, has not been considered by philosophers before as a central theoretical criterion (as far as I know). But it is used by scientists all the time.

I am not sure if this is the first paper to analyze a scientific revolution based on avoiding certain types of fine-tuning. Inflation is not the first case--- Lorentz ether models are "fine tuned" compared to relativity, and geocentric models are fine-tuned compared to heliocentric models. But with inflation, avoiding fine-tuning is all the guidance that you've got, really, so this makes it a clean case.

But the paper makes a few mistakes, and these should not be glossed over. The no-hair theorem for deSitter space is both true and obvious to the specialists. It follows from the geodesic separation, if you like, from the inflation, and from the exponential decay of all perturbations. This theorem is much easier than the corresponding black hole no hair theorem, which might explain why they had a hard time tracking it down in the physics literature. It is considered too obvious by itself to devote too much time to, and it is implicit in the analysis of cosmological perturbations, since these always decay during inflation (except for residual quantum fluctuations). The decay of perturbations is analyzed in books today, but it was known in the literature back in 1999 too.

Their belief that the final value of lambda0 is zero is a fine tuning is also wrong--- this is the whole point of inflation. I think they just were confused about definitions, perhaps because they were reading about FRW models too much, not about deSitter models. But these mistakes don't detract from their main point, which is that the fine tuning of inflation models is no better than the fine tuning of FRW initial conditions, and I think it is safe to say that nearly no cosmologists agree with that, but it is an interesting thing for philosophers to try to figure out why.Likebox (talk) 19:08, 30 April 2009 (UTC)

Local/Global

The inflation literature generally calculates from the General Relativity point of view, which has global time slices. The volume of the universe expands exponentially during inflation, then the previously inflated regions come into view during the normal FRW expansion. This led to philosophical discomfort, Guth notes that if you think of regions of space which occupy a bigger volume in one spatial slice as more "likely" in some probability sense, then you would expect that the universe should never want to stop inflating. There are exponentially many more regions where inflation is still going on than regions where it has stopped, so if you assign regions a probability based on volume, you would expect that regions with more inflation are vastly more likely than regions with less.

This leads to paradoxical conclusions, as Guth pointed out. The universe should, in this probabilistic point of view, want to maximize the time it spends inflating. This means that the universe should be absurdly fine tuned to maximize this time. This can be phrased in terms of the "improbability per unit time". Ending inflation costs a certain amount in improbability (as measured by volume ratio), so this can be fixed by speeding up evolution to our current state by introducing improbable events: like for example, instead of evolving life slowly by a reasonable process of evolution, maybe it pays off to have a few extra billion years of inflation, and a very improbable fluctuation that produces all life on earth by a big improbable thermodynamic fluctuation. This lets you predict that we are the only solar system in the universe, the only life in the universe, etc, etc, and all sorts of other things that never happened.

Since there doesn't seem to be a huge amount of improbability-per-second in the evolution of the universe, weighting regions by volume can't be right. The local point of view allows you to intoduce different weighting--- by following one observer, you can say that the probability of a universe is proportional to the probability of its occurence in the frame of the observer. This resolves the paradoxes. I personally learned this point of view from Polchinski, but it must be shared by large parts of the string cosmology community. I don't know this literature well enough to find the original source.Likebox (talk) 19:46, 7 May 2009 (UTC)

Boltzmann Brain may have the answers / refs / links. --Michael C. Price ^talk 05:31, 23 May 2009 (UTC)

Yes, the Boltzmann brain is the same thing in the pre-inflation context. Its all similar ideas.

What I don't know how to source very well is the statement that the probability of a patch of space is not proportional to the volume of the patch, but of the probability of occurence along the world-line of an observer. Those are not the same for inflationary models. The volume weighting gives eternal inflation, the observer weighting doesn't.Likebox (talk) 19:45, 26 May 2009 (UTC)

Inflation by how much?

I came here looking for some numbers: inflation, by how much, and for how long? Is it 10^20, 10^50, 10^100? I know, from what I've read above, that this has no simple answer, but at least a small paragraph by the experts on the most accepted values in research papers would go a long way.

The length of inflation is usually expressed in the number of e-foldings, i.e. then number of factors of e by which the scale factor increases. To solve the flatness problem this needs to be at least 60. So, the size of the universe must have increased by at least a factor e^60 ~ 10^26. But it may have lasted much longer than that (or even infinitely long); it is not possible at the time to put an upperlimit on the value. I'll see what I can do about adding something along these lines to the article.(TimothyRias (talk) 09:30, 18 August 2009 (UTC))

$10^{26}-\infty$ sounds fine to me.--Michael C. Price ^talk 09:42, 18 August 2009 (UTC)

Our article on the inflationary epoch agrees: "This rapid expansion increased the linear dimensions of the early universe by a factor of at least 10²⁶ (and possibly a much larger factor), and so increased its volume by a factor of at least 10⁷⁸". Gandalf61 (talk) 11:25, 18 August 2009 (UTC)

Graceful exit

The issue of the graceful exit is mentioned in the introductory paragraphs, but never dealt with in the main article itself. For a layperson like myself, who has come to the article to understand something, I am left still clueless about the significance of the graceful exit to inflation.-- spin^control 03:13, 9 September 2009 (UTC)

Graceful exit is adressed under another name: it is called "new inflation". The significance is that old inflation models would produce bubbles of vacuum, like nucleation of steam in super-heated water, leading to matter concentrated on the surface of the bubbles, very inhomogeneously. The new inflation has a smooth inflation dynamics, so that the energy is produced everywhere in the same amounts. Please fix the article by adding a sentence saying that the two are equivalent at the point where you got confused.Likebox (talk) 00:26, 10 September 2009 (UTC)

Thank you. Shouldn't the information be included in the article? -- spin^control 15:58, 22 September 2009 (UTC)

Please put it in--- I don't know exactly where it got confusing.Likebox (talk) 23:03, 22 September 2009 (UTC)

Lead section - Too many names

In my opinion, science articles should contain information in the lead section similar to the abstract of a research article. Just describe what the article is about. I'm uncomfortable with naming names in the lead section because what I'm looking for is an article summary. Unnecessarily naming names to me looks like promoting personalities instead of explaining things. Yes, name names in the article, because those persons are noteworthy for the work they did to establish this theory, but it's the theory itself that should IMO be the subject of the lead section, unless there is some major controversy attached to the theory that needs to be explained to put the rest of the article in context. Dcs002 (talk) 22:29, 30 October 2009 (UTC)

Agreed. And removed. All the details appeared later in the article. Lead was too long and specific. --Michael C. Price ^talk 23:45, 30 October 2009 (UTC)