Talk:Flatness problem

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Former good article nominee Flatness problem was a Natural sciences good articles nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Article milestones
Date Process Result
September 25, 2008 Good article nominee Not listed
Did You Know


Okay, here's something I ought to understand but don't, and would like some clarification of.

The critical density at which the expansion rate of the universe will tend asymptotically towards zero is about 1×10^-29 grammes per cubic centimeter, and the ratio of the actual density of the universe to this value is known as Ω.

This value of 1x10^-29 g/cm presumably must either be a function of time, or rather of the size of the universe, or be measured in some sort of co-moving coordinate system in which a cm today is larger than a cm yesterday, right? Otherwise, if the density were slightly above 1x10^-29 g/cm early in the history of the universe, it would fall below that value as the universe expands, and you'd go from a universe that's supposed to fall back into a big crunch to a universe that is supposed to expand forever, and that makes no sense.

Currently, observations indicate that Ω is between 0.98 and 1.06 - in other words, that the universe's density is very close to or exactly the critical value. ... The fact that approximately 14 billion years after its formation, the universe still has an Ω so close to unity indicates that Ω must have been within one part in 10^15 of unity when the universe formed.

Is it the case that in a matter dominated universe, Ω is constant? If it isn't, how can it vary? And in a universe with dark matter, Ω does evolve... right? -- Rsholmes 18:40, 20 February 2006 (UTC)

For crying out loud, this article doesn't deal with the flatness problem almost at all! There's a lot of Big Bang theory and inflationary universe, but what does it mean "flatness"? How are these theories related to it? How can we tell or observe if the universe is flat or not, from our POV? This should be merged somewhere else and the article rewritten from scratch or so.
  • The article's actually okay, if a little jargon-y and not very in-depth. I'll try and tackle it a bit later. WilyD 23:15, 21 December 2006 (UTC)
2nd the motion -the diagram with 3 images do nothing to illustrate flatness! Juror1 (talk) 07:54, 29 February 2016 (UTC)
The article assumes that one knows what "critical density" is. The link, which points to Friedmann equations is not very helpful. Maybe someone can explain "critical density" in simple terms. —Preceding unsigned comment added by (talk) 15:37, 14 May 2008 (UTC)
I've just begun working on a new version of this article. I'll try and explain that (among other things) more clearly. Olaf Davis | Talk 16:31, 14 May 2008 (UTC)

Evolution of density[edit]

I'm glad to see some work being done on this article. I'd still like to better understand the evolution of Ω. In universe without dark energy / cosmological constant, is Ω constant in time? It would seem as though the answer must be no, and the article seems to suggest that. But what is the mechanism for this evolution? -- Rsholmes 23:46, 22 December 2006 (UTC)

  • Okay, I can try to make that clearer - the article is only talking about Ω today. If Ω is less than one, then in the past it was larger (but still less than one), similarly if it's greater than one at the big bang, it gets larger as time goes on. But I'll have to do some math or research to address the issue for generic universes.
  • Generally, the density of radiation decreases as the fourth power of the redshift, or the fourth power of the scale factor of the universe. For matter, it's the third power (and this is the easiest to understand, as matter density is just mass/volume, volume is the third power of distance, and distance is just a constant times the scale factor. Curvature, if thought of as having a Ω component, goes as the second power of Ω, and Dark Energy doesn't depend on Ω (assuming w = -1 for Dark Energy, which isn't shown, but is probably true. Nonetheless, everyday astro-ph has a paper or two on w maybe isn't -1, so ... WilyD 16:08, 23 December 2006 (UTC)
  • Actually, if you can give me a lot of feedback on what's confusing, I can try to make the article clearer. I understand the flatness problem okay, but I'm not a great communicator without jestures, and I'm not really aware of the sticking points of this, as I've never taught or even TA'd a cosmology course. WilyD 16:12, 23 December 2006 (UTC)


I've just done a complete rewrite of the article I'd been working on in user space for a while. There are still some things left on my to-do list, but it seemed ready for mainspace. Here are some things I'll try and work on - feel free to give a hand!

  • Why physicists dislike the AP - Anthropic Explanations has some on this.
  • Discuss dark energy? Not much to say but it might be nice
  • Include some stuff on recent developments - some of these [1] look promising
  • Add a second diagram including the inflationary era
  • [2] claims it wasn't discovered until 1979 - some further sources to confirm one of the dates would be nice
  • Non-breaking spaces are needed in a few places for equations  Done

Olaf Davis | Talk 11:21, 7 September 2008 (UTC)

GA Review[edit]

This review is transcluded from Talk:Flatness problem/GA1. The edit link for this section can be used to add comments to the review.

Protonk comments[edit]


  • Image:End of universe.jpg doesn't provide source information (Aside from a name). This is the source. It is also my opinion that this image should be moved up to the top of the article.
Source added, and image moved. Olaf Davis | Talk 16:38, 10 September 2008 (UTC)
But that image is showing something else: size of the universe vs. time for different matter/dark energy compositions. The current one shows the density parameter vs.time for different total densities to indicate how it diverges from 1. Olaf Davis | Talk 07:52, 9 September 2008 (UTC)


  • Citation method is inconsistent. The citations should appear in the same format, but I don't care what that format is.
  • Citations (if the notes layout is used, versus the notes/refs layout) should cite the work in a manner that allows the reader to find the source, then following citations of the same material can be abbreviated. Stompor et al 2001 is cited in an abbreviated fashion only.
Fixed. Olaf Davis | Talk 16:29, 10 September 2008 (UTC)

MOS issues[edit]

  • "The flatness problem is a cosmological fine-tuning problem within the Big Bang model." Per WP:LEAD this sentence should probably be rewritten a bit to include the discipline more explicitly.
Done. Olaf Davis (talk) 18:02, 19 June 2009 (UTC)
  • Fine-tuning is linked twice in the lead.
Fixed. Olaf Davis | Talk 07:50, 9 September 2008 (UTC)
  • The first citation in the lead is not necessary. The second might be.
Removed first cite. Olaf Davis | Talk 07:50, 9 September 2008 (UTC)
  • the lead should be longer.
Done. Olaf Davis (talk) 18:02, 19 June 2009 (UTC)
  • Energy Density and Spacetime Curvature section titles shouldn't be capitalized.
Fixed. Olaf Davis | Talk 07:50, 9 September 2008 (UTC)
  • Current Value of Ω Same same
Fixed. Olaf Davis | Talk 07:50, 9 September 2008 (UTC)

Non MOS issues[edit]

  • "The flatness problem arises because of the effect which the density of the universe has on its geometry..." This sentence is awkwardly worded.
It seems to have disappeared at some point. Olaf Davis (talk) 17:29, 19 June 2009 (UTC)
  • "Since the total energy density of the universe departs rapidly from the critical value over cosmic time,[2] the early universe must..." Jumps into detail WAY too fast. Think of the lead as an executive summary. Anyone, regardless of training, should be able to read it and give a good summary of the article contents. I don't mean that the lead should be oversimplified, but the explanatory summary in the article should have its best elements used in the lead summary.
I've had a go at rewriting this - hopefully it's clearer to the layman now. Olaf Davis (talk) 17:29, 19 June 2009 (UTC)
  • Fine-tuning, if linked prominently from this article, should be improved, or at least sourced.
Is that really a requirement for GA status? As far as I was aware even FAs weren't held to that standard... Olaf Davis (talk) 17:29, 19 June 2009 (UTC)
  • Energy Density and Spacetime Curvature This should be merged with the following section.
Done, it seems. Olaf Davis (talk) 17:29, 19 June 2009 (UTC)
  • "One such observation is that of anisotropies in the Cosmic Microwave Background (CMB) radiation..." This sentence and the sentence that preceeds it aren't very helpful. The two paragraphs describing experimental validation of background lensing should be rewritten to better describe what it is and how it offers a look at the value of Ω.
  • "This tiny value is the crux of the flatness problem..." This paragraph should start a new section.
Fixed. Olaf Davis (talk) 17:29, 19 June 2009 (UTC)
  • "Some cosmologists agreed with Dicke..." Who?
  • "But there was also a school of thought..." What school of thought? Who were its adherents?
  • "Enough cosmologists saw the problem as a real one..." How many is enough? And who?
  • "...for various reasons to be proposed." Remember, when writing, don't say you are going to do something, do it. If you need to mention that you will introduce possible "reasons", just introduce them in a short summary.
I think you've misinterpreted what I meant. I've reworded it. Olaf Davis (talk) 17:29, 19 June 2009 (UTC)
  • Criticisms of the Anthropic Principle No need for this header. Just include the criticism in the prose.
Done. Olaf Davis (talk) 17:29, 19 June 2009 (UTC)
  • "Since many physicists and philosophers of science do not consider the principle to be compatible with the scientific method..." The article can and should state clearly why the anthropic principle is not compatible with the scientific method.
  • "...another explanation for the flatness problem was needed." I am of the opinion that this kind of a segue should only be used if the failure of the anthropic principle to explain this anomaly is what spurred the inflation principle. Is that what happened? Or did a set of people consider the anthropic principle sufficient to explain this particular issue and another set of people work in parallel on a more testable proposition?
  • "The idea of inflation was first thought of..." a stronger verb is needed here.
Changed to 'proposed'. Olaf Davis (talk) 16:47, 19 June 2009 (UTC)
  • "This solving of the flatness problem is considered one of the major motivations for the existence of an inflationary epoch." What does this mean?
Reworded to "This success in solving the flatness problem is considered one of the major motivations for inflationary theory." Olaf Davis (talk) 16:47, 19 June 2009 (UTC)
  • "These have included non-standard interpretations..." What does non-standard mean in this context?
  • As a matter of fact, the "Post inflation" section should be fleshed out and explained fully.
  • In the post inflation section, is it fair to say that dark energy and dark matter are still to be treated as heterodox?
It wasn't my intention to imply that they are. In fact I'm not quite sure that the text does imply that. Olaf Davis (talk) 13:42, 20 June 2009 (UTC)
What about him do you think needs mentioning? Olaf Davis (talk) 13:42, 20 June 2009 (UTC)
  • "... as the scale factor grows exponentially" Does it grow exponentially or is this just a turn of phrase?
It's actually exponential. I've tried to clarify this by explicitly saying a ~ exp (t) above. Olaf Davis (talk) 13:42, 20 June 2009 (UTC)
  • The explanation of the Friedmann equation and the resulting expected values for should be clarified and expressed more formally. Step the reader through the derivation, even it if appears simple. You rely on their intuitive understanding of this formula later in the article, so don't rush past this.


This article is a good attempt at explaining a rather esoteric problem to a general audience but it has a few major problems. First (and this is the root of the other problems), it is too short to cover the subject appropriately. Second, it doesn't provide sufficient context for the subject. I can't judge the article POV because I have little information about the history of the problem among the community of physicists and the status of the solutions among the same. Third, the article has a spotty expectation of reader familiarity of the subject. Let's take these one by one:

  1. too short/little context. The article can spend some more time discussing the roots of the flatness problem including what people thought at the time about it. There are several histories of science that cover the topic in some detail out there. the article can also spend some more time on solutions to the problem. The cosmic inflation section shouldn't get too long, lest it needlessly recapitulate detail elsewhere, but the post inflation solution section can be broken up and explanded. Likewise with the explanation of EFE and the curvature of space. The Freidmann equation can be laid out more fully and then the dark energy terms dispensed with (with some explanation why this was done). Likewise the article should make clear why this is a problem for physicists. It isn't an anomaly, in the Kuhnian sense. It is more of a curiosity until you look closer. Explain how we understood cosmology at the time and why a formula for the density of space could create such a fuss. Crucial to this is explaining the problem of divergence. This is partially why I suggested an image change. Other physicists need a mention here (some are noted above).
  2. Reader familiarity. Assume that your reader is willing to click on well targeted wikilinks in order to understand an article. Don't talk down but don't speak entirely in the language of the discipline. I understand that this is not a particularly difficult concept as presented but the explanation of it should still proceed step by step. This is more of a clarity issue than a difficulty level issue. You will find that if you take the time and space to be clear, the level of material that can be presented will be increased.

I'm going to place this article on hold. The problems this article has to overcome are significant but not insurmountable. If they aren't one in ~7 days, no one should be ashamed if this article is not listed. The problems can be fixed and this article will be a GA soon. If not in the next seven days than soon thereafter. Thanks for giving me the chance to review an article like this. Protonk (talk) 03:47, 9 September 2008 (UTC)

Thanks for the very detailed review Protonk! I'll try and address your points soon. I probably won't have time to get to all of them this week, but it's not like there's a rush. Olaf Davis | Talk 07:45, 9 September 2008 (UTC)
  • No rush. the week thing is more for you than for me. It stops me from putting an article on hold and then indefinitely refusing to promote it. Protonk (talk) 13:47, 9 September 2008 (UTC)

Not promoting[edit]

I know there is no rush, but holding this article for 15 days is a little much. I would probably feel differently if the issues were being actively addressed, but it has been 9 days since the last change to the article. This article has a lot of potential but it isn't a good article yet. If you disagree with this decision feel free to post here or on my talk page. If you feel it was flagrantly unacceptable, you may bring this article to Good Article Review. Thank you and better luck in the future. Protonk (talk) 04:34, 25 September 2008 (UTC)

No, that's perfectly reasonable. I would have been addressing them more actively but I've had scant internet access recently - hopefully that will change soon and I can get back to work. Olaf Davis | Talk 22:04, 25 September 2008 (UTC)

My edit to Current value of Ω[edit]

Originally, the article stated that:

Data from the Wilkinson Microwave Anisotropy Probe (measuring CMB anisotropies) combined with that from the Sloan Digital Sky Survey (observing Ia supernovae) constrain Ω0 to be 1 within 1%.

This is misleading because the main contribution of SDSS to measuring the spatial flatness is through the galaxy power spectrum and it is this data that was used in the study cited. Although, as Olaf Davis pointed out in his edit summary, the SDSS telescope has been used more recently to find type-1a supernovae [3], this data was not used in the study cited. Even if it had been, it would be misleading to single it out for mention, since the Sloan Supernova Survey data form only a part of the overall sample of supernovae with measured redshifts.

I changed the above sentence to read:

Data from the Wilkinson Microwave Anisotropy Probe (measuring CMB anisotropies) combined with that from the Sloan Digital Sky Survey and observations of type-Ia supernovae constrain Ω0 to be 1 within 1%.

I think this is a more accurate description - at least of the study cited. I'll admit to being out of the loop for the past year though, so if anyone knows of a more recent study in which spatial flatness has been measured to a higher degree of accuracy using only WMAP data and type-1a supernovae, then please update the citation.

Cosmo0 (talk) 22:52, 15 September 2009 (UTC)

Good point. I reverted your edit when I saw the summary said the SDSS didn't observe SNae, without thinking to check what the particular citation was about. Sorry! Olaf Davis (talk) 19:09, 16 September 2009 (UTC)

Geometric problem with the diagram[edit]

The first diagram that shows three different geometries based on curvature: positive, negative and flat. For each of these geometries, a triangle is shown. The triangle for the negative curvature is wrong. The sum of the degrees for the three angles in a triangle on these three geometric surfaces should be respectively: >180, <180, =180. The triangle shown for the negative curvature erroneously has a angles adding to >180, like the positive curvature triangle. BuzzBloom (talk) 13:34, 17 March 2015 (UTC) BuzzBloom

Mistake and correction[edit]

Universal flatness is the law. Other artefacts are secondary. All the data suggest that the universal flatness is fundamental.Dark Matter, Dark Energy and Big Bangs are secondary effects that urge to maintain that permanent flatness. Some people like mistakes because are weird. A mistake is always stupid and against the data though. — Preceding unsigned comment added by 2A02:587:4103:AE00:D47:B687:8172:7D1E (talk) 23:13, 1 July 2016 (UTC)