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A non-standard cosmology is any physical cosmological model of the universe that has been, or still is, proposed as an alternative to the Big Bang model of standard physical cosmology. In the history of cosmology, various scientists and researchers have disputed parts or all of the Big Bang due to a rejection or addition of fundamental assumptions needed to develop a theoretical model of the universe. From the 1940s to the 1960s, the astrophysical community was equally divided between supporters of the Big Bang theory and supporters of a rival steady state universe. It was not until advances in observational cosmology in the late 1960s that the Big Bang would eventually become the dominant theory, and today there are few active researchers who dispute it.
The term non-standard is applied to any cosmological theory that does not conform to the scientific consensus, but is not used in describing alternative models where no consensus has been reached, and is also used to describe theories that accept a "big bang" occurred but differ as to the detailed physics of the origin and evolution of the universe. Because the term depends on the prevailing consensus, the meaning of the term changes over time. For example, hot dark matter would not have been considered non-standard in 1990, but would be in 2010. Conversely a non-zero cosmological constant resulting in an accelerating universe would have been considered non-standard in 1990, but is part of the standard cosmology in 2010.
Fundamental assumptions for building a cosmology 
Before observational evidence was gathered, theorists developed frameworks based on what they understood to be the most general features of physics and philosophical assumptions about the universe. When Albert Einstein developed his general theory of relativity in 1915, this was used as a mathematical starting point for most cosmological theories including the Big Bang and the Steady State theories. In order to arrive at a cosmological model, however, theoreticians needed to make assumptions about the nature of the largest scales of the universe. The assumptions that the Big Bang relied upon are:
- the universality of physical laws – that the laws of physics don't change from one place and time to another,
- the cosmological principle – that the universe is roughly homogeneous and isotropic in space though not necessarily in time, and
- the Copernican principle – that we are not observing the universe from a preferred locale.
These assumptions when applied to the Einstein field equations naturally result in a universe which has the following features:
- an expansion of the universe,
- the universe emerging from a hot, dense state at a finite time in the past,
- the lightest elements were created in the first moments that time existed as we know it, and
- a cosmic microwave background pervading the entire universe should exist, which is a record of a phase transition that occurred when the atoms of the universe first formed.
Finally, one might adduce a variation of the Ontological Argument. As Richard Feynman put it, "In physics anything that is not forbidden is compulsory": the Universe exists because it can. According to this argument, since this has always been the case there must always have been a Universe – i.e. the Universe is without beginning or end.
These features were derived by numerous individuals over a period of years; indeed it was not until the middle of the twentieth century that accurate predictions of the last feature and observations confirming its existence were made. Non-standard theories developed either by starting from different assumptions or by contradicting the features predicted by the Big Bang.
Modern physical cosmology as it is currently studied first emerged as a scientific discipline in the period after the Shapley–Curtis debate and discoveries by Edwin Hubble of a cosmic distance ladder when astronomers and physicists had to come to terms with a universe that was of a much larger scale than the previously assumed galactic size. Theorists who successfully developed cosmologies applicable to the larger-scale universe are remembered today as the founders of modern cosmology. Among these scientists are Arthur Milne, Willem de Sitter, Alexander Friedman, Georges Lemaitre, and Albert Einstein himself.
After confirmation of the Hubble's law by observation, the two most popular cosmological theories became the Steady State theory of Hoyle, Gold and Bondi, and the big bang theory of Ralph Alpher, George Gamow, and Robert Dicke with a small number of supporters of a smattering of alternatives. Since the discovery of the Cosmic microwave background radiation (CMB) by Penzias and Robert Wilson in 1965, most cosmologists concluded that observations were best explained by the big bang model. Steady State theorists and other non-standard cosmologies were then tasked with providing an explanation for the phenomenon if they were to remain plausible. This led to original approaches including integrated starlight and cosmic iron whiskers which were meant to provide a source for a pervasive, all-sky microwave background that was not due to an early universe phase transition.
Skepticism about the non-standard cosmologies' ability to explain the CMB caused interest in the subject to wane ever since, however, there have been two periods in which interest in non-standard cosmology has increased due to observational data which posed difficulties for the big bang. The first occurred was the late 1970s when there were a number of unsolved problems such as the horizon problem, the flatness problem, and the lack of magnetic monopoles challenged the big bang model. These issues were eventually resolved by cosmic inflation in the 1980s. This idea subsequently became part of the understanding of the big bang, although alternatives have been proposed from time to time. The second occurred in the mid-1990s when observations of the ages of globular clusters and the primordial helium abundance apparently disagreed with the big bang. However, by the late 1990s, most astronomers had concluded that these observations did not challenge the big bang and additional data from COBE and WMAP provided detailed quantitative measures which were consistent with standard cosmology.
In the 1990s, a dawning of a "golden age of cosmology" was accompanied by a startling discovery that the expansion of the universe was, in fact, accelerating. Previous to this, it had been assumed that matter either in its visible or invisible dark matter form was the dominant energy density in the universe. This "classical" big bang cosmology was overthrown when it was discovered that nearly 70% of the energy in the universe was tied up in a mysterious and difficult to characterize form of dark energy. This has led to the development of a so-called concordance ΛCDM model which combines detailed data obtained with new telescopes and techniques in observational astrophysics with an expanding, density-changing universe. Today, it is more common to find in the scientific literature proposals for "non-standard cosmologies" that actually accept the basic tenets of the big bang cosmology, while modifying parts of the concordance model. Such theories include alternative models of dark energy, such as quintessence, phantom energy and some ideas in brane cosmology; alternative models of dark matter, such as modified Newtonian dynamics; alternatives or extensions to inflation such as chaotic inflation and the ekpyrotic model; and proposals to supplement the universe with a first cause, such as the Hartle–Hawking boundary condition, the cyclic model, and the string landscape. There is no consensus about these ideas amongst cosmologists, but they are nonetheless active fields of academic inquiry.
Today, heterodox non-standard cosmologies are generally considered unworthy of consideration by cosmologists while many of the historically significant nonstandard cosmologies are considered to have been falsified. The essentials of the big bang theory have been confirmed by a wide range of complementary and detailed observations, and no non-standard cosmologies have reproduced the range of successes of the big bang model. Speculations about alternatives are not normally part of research or pedagogical discussions except as object lessons or for their historical importance. An open letter started by some remaining advocates of non-standard cosmology has affirmed that: "today, virtually all financial and experimental resources in cosmology are devoted to big bang studies...."
Non-standard cosmologies 
Non-standard cosmologies can be grouped according to the assumptions or the features of the big bang universe which they contradict.
Alternative metric cosmologies 
The Friedmann–Lemaître–Robertson–Walker metric that is necessary for the Big Bang and Steady State models emerged in the decade after the development of Einstein's general relativity and was accepted as a model for the universe after Edwin Hubble's discovery of his eponymous law. It was not clear early on how to find a "universe solution" to Einstein's equations that allowed for a universe that was infinite, unending, and immutable (scientists of the time assumed for philosophical reasons the universe should have such a character). Even after the development of expanding universe theories, people would engage in this exercise from time to time when looking for a replacement for general relativity. Any alternative theory of gravity would imply immediately an alternative cosmological theory since current modeling is dependent on general relativity as a framework assumption. What is included are a number of models based on alternative gravitational scenarios as well as early attempts to derive cosmological solutions from relativity.
Newtonian cosmology 
While not seriously advocated after Einstein's development of relativity, Newtonian gravity can be used to model the universe and non-rigorously derive the Friedmann equations that are used in the big bang universe. This non-standard cosmology is mostly used as an elementary exercise for astronomy and physics students and doesn't represent a serious alternative proposal.
Lorentzian universes 
Before the complete development of general relativity, Arthur Milne offered a cosmology based on Lorentz transformations which had the feature of being applicable to a universe of any scale. It relied on a rejection of the curvature of space and so contradicted predictions from general relativity about the shape of the universe caused by the mass it contains. Milne's universe is still used today as a model of a hypothetical "empty universe".
Early general relativity based cosmologies 
Before the present general relativistic cosmological model was developed, Albert Einstein proposed a way to dynamically stabilize a cosmological scenario that would necessarily collapse in on itself due to the gravitational attraction of the matter constituents in the universe. Such a universe would need a source of "anti-gravity" to balance out the mutual attraction, a scalar term in Einstein's equations that would come to be known as the cosmological constant. Einstein's first attempt at modeling relied on a cosmological constant that was finely tuned to exactly balance out matter curvature and provide a framework for an infinite and unchanging spacetime metric in which the objects of the universe were embedded. This happens to be the same as a special case of the current cosmological model where the cosmic scale factor is unchanging and the density seen in the Friedmann equations is equally divided between the cosmological constant and matter.
Willem de Sitter would later generalize Einstein's scalar potential model to a universe model that would expand exponentially. As the early development of the Big Bang theory began, De Sitter would be falsely credited for inventing the expanding universe metric because of this. In reality, it was the work of Alexander Friedman and Georges Lemaître who established the metric that would come to be the most accepted for cosmology. Nevertheless, De Sitter's model appears in two places today: in the discussion of cosmic inflation and in the discussion of dark energy dominated universes.
Machian universe 
Ernst Mach developed a kind of extension to general relativity which proposed that inertia was due to gravitational effects of the mass distribution of the universe. This led naturally to speculation about the cosmological implications for such a proposal. Carl Brans and Robert Dicke were able to successfully incorporate Mach's principle into general relativity which admitted for cosmological solutions that would imply a variable mass. The homogeneously distributed mass of the universe would result in a roughly scalar field that permeated the universe and would serve as a source for Newton's gravitational constant; creating a theory of quantum gravity.
Gödel's universe 
Partly as a counter-example to Mach's principle, Kurt Gödel found a solution to the Einstein field equations describing a universe with a non-zero angular momentum. This cosmology contained closed timelike curves; a signal or object starting from an event in such a universe could return to the same event. Einstein was unsatisfied with the implications of this and abandoned his hope for incorporating Mach's Principle into general relativity. Because of this effect, astronomers can in principle put limits on the rotation rate of the universe which today is measured to be close enough to zero that no cosmological implications should be expected.
Modified Newtonian Dynamics (MOND) is a relatively modern proposal to explain the galaxy rotation problem based on a variation of Newton's Second Law of Dynamics at low accelerations. This would produce a large-scale variation of Newton's universal theory of gravity. A modification of Newton's theory would also imply a modification of general relativistic cosmology in as much as Newtonian cosmology is the limit of Friedman cosmology. While almost all astrophysicists today reject MOND in favor of dark matter, a small number of researchers continue to enhance it, recently incorporating Brans–Dicke theories into treatments that attempt to account for cosmological observations.
Tensor–vector–scalar gravity (TeVeS) is a proposed relativistic theory that is equivalent to Modified Newtonian dynamics (MOND) in the non-relativistic limit, which purports to explain the galaxy rotation problem without invoking dark matter. Originated by Jacob Bekenstein in 2004, it incorporates various dynamical and non-dynamical tensor fields, vector fields and scalar fields.
The break-through of TeVeS over MOND is that it can explain the phenomenon of gravitational lensing, a cosmic optical illusion in which matter bends light, which has been confirmed many times. A recent preliminary finding is that it can explain structure formation without CDM, but requiring a ~2eV massive neutrino (They are also required to fit some Clusters of galaxies, including Bullet Cluster)  and . However, other authors (see Slosar, Melchiorri and Silk ) claim that TeVeS can't explain cosmic microwave background anisotropies and structure formation at the same time, i.e. ruling out those models at high significance.
Steady State theories 
The Steady State theory was proposed in 1948 by Fred Hoyle, Thomas Gold, Hermann Bondi and others as an alternative to the Big Bang theory that modified the homogeneity assumption of the cosmological principle to reflect a homogeneity in time as well as in space. This "perfect cosmological principle" as it would come to be called predicted a universe that expanded but did not change its density. In order to accomplish this, steady state cosmology had to posit a "matter-creation field" (the so-called C-field) that would insert matter into the universe in order to maintain a constant density.
The idea was almost immediately attacked by proponents of the Big Bang who described the C-field as contradictory to a consistent understanding of physics. Hoyle, one of the most vocal proponents of the steady state model, and a committed materialist, believed that the competing, older model was forced as it violated fundamental philosophical principles regarding the infinite nature of existence. Hoyle explicitly warned that the Big Bang was being promoted as a first cause dogma in line with Western theology rather than science. To attack the connection, Hoyle began a public campaign to discredit the Big Bang theory and wound up coining the term "Big Bang" which remains stuck to the standard cosmological theory today, though the descriptive quality of the name has heavily been criticized as being misleading.
The debate between the Big Bang and the Steady State models would happen for 15 years with camps roughly evenly divided until the discovery of the cosmic microwave background radiation. This radiation is a natural feature of the Big Bang model which demands a "time of last scattering" where photons decouple with baryonic matter. The Steady State model proposed that this radiation could be accounted for by so-called "integrated starlight" which was a background caused in part by Olbers' paradox in an infinite universe. In order to account for the uniformity of the background, steady state proponents posited a fog effect associated with microscopic iron particles that would scatter radio waves in such a manner as to produce an isotropic CMB. The proposed phenomena was whimsically named "cosmic iron whiskers" and served as the thermalization mechanism. The Steady State theory did not have the horizon problem of the Big Bang because it assumed an infinite amount of time was available for thermalizing the background.
As more cosmological data began to be collected, cosmologists began to realize that the Big Bang correctly predicted the abundance of light elements observed in the cosmos. What was a coincidental ratio of hydrogen to deuterium and helium in the steady state model was a feature of the Big Bang model. Additionally, detailed measurements of the CMB beginning in the 1990s indicated that the spectrum of the background was closer to a blackbody than any other source in nature. The best integrated starlight models could predict was a thermalization to the level of 10% while the COBE satellite measured the deviation at one part in 105. After this dramatic discovery, the majority of cosmologists became convinced that the steady state theory could not explain the cosmological observations as well as the Big Bang. Since that time, detailed observations of WMAP have isolated a standard Lambda-CDM model which relates the anisotropies in the CMB to features in the universe such as large-scale structure, the detailed nature of Hubble's law, and even bizarre features such as inflation, dark energy, and cold dark matter.
Although the original steady state model is now considered to be contrary to observations even by its one-time supporters, a modification of the steady state model has been proposed, which envisions the universe as originating through many little bangs rather than one big bang. It supposes that the Universe goes through periodic expansion and contraction phases, with a soft "rebound" in place of the Big Bang. Thus the redshift is explained by the fact that the Universe is currently in an expansion phase. A handful of remaining steady state theorists (most famously Jayant V. Narlikar) continue to insist that the intergalactic medium contains cosmic iron whiskers. However, there is still no corroborating observational evidence for the existence of these iron particles.
Proposals based on observational skepticism 
As the observational cosmology began to develop, certain astronomers began to offer alternative speculations regarding the interpretation of various phenomena that occasionally became parts of non-standard cosmologies.
Tired light 
The tired light effect was proposed by Fritz Zwicky in 1929 as a possible alternative explanation for the observed cosmological redshift. The basic proposal amounted to light losing energy ("getting tired") due to the distance it traveled rather than any metric expansion or physical recession of sources from observers. A traditional explanation of this effect was to attribute a dynamical friction to photons; the photons' gravitational interactions with stars and other material will progressively reduce their momentum, thus producing a redshift. Other proposals for explaining how photons could lose energy included the scattering of light by intervening material in a process similar to observed interstellar reddening. However, all these processes would also tend to blur images of distant objects, and no such blurring has been detected.
Traditional tired light has been found incompatible with the observed time dilation that is associated with the cosmological redshift. This idea is mostly remembered as a falsified alternative explanation for Hubble's law in most astronomy or cosmology discussions.
Dirac large numbers hypothesis 
The Dirac large numbers hypothesis uses the ratio of the size of the visible universe to the radius of quantum particle to predict the age of the universe. The coincidence of various ratios being close in order of magnitude may ultimately prove meaningless or the indication of a deeper connection between concepts in a future theory of everything. Nevertheless, attempts to use such ideas have been criticized as numerology.
Redshift periodicity and intrinsic redshifts 
A minority of astrophysicists has been unconvinced that the cosmological redshifts are associated with a universal cosmological expansion. Skepticism and alternative explanations began appearing in the scientific literature in the 1960s. In particular, Geoffrey Burbidge, William Tifft and Halton Arp were all observational astrophysicists who proposed that there were inconsistencies in the redshift observations of galaxies and quasars. The first two were famous for suggesting that there were periodicities in the redshift distributions of galaxies and quasars. Close statistical analyses of redshift surveys today seem to indicate that there is no more periodicity than can be accounted for by large-scale structure of the cosmos.
During the quasar controversies of the 1970s, these same astronomers were also of the opinion that quasars exhibited high redshifts not due to their incredible distance but rather due to unexplained intrinsic redshift mechanisms that would cause the periodicities and cast doubt on the Big Bang. Arguments over how distant quasars were took the form of debates surrounding quasar energy production mechanisms, their light curves, and whether quasars exhibited any proper motion. Astronomers who believed quasars were not at cosmological distances argued that the Eddington luminosity set limits on how distant the quasars could be since the energy output required to explain the apparent brightness of cosmologically-distant quasars was far too high to be explainable by nuclear fusion alone. This objection was made moot by the improved models of gravity-powered accretion disks which for sufficiently dense material (such as black holes) can be more efficient at energy production than nuclear reactions. The controversy was laid to rest by the 1990s when evidence became available that indicated quasars were actually the ultra-luminous cores of distant active galactic nuclei and that the major components of their redshift were in fact due to the Hubble flow.
Halton Arp continues to maintain that there are anomalies in his observing of quasars and galaxies that serve as a refutation of the Big Bang. Arp has made observations of correlations between quasars and (relatively) nearby AGN claiming that clusters of quasars have been observed in alignment around AGN cores. Arp believes that quasars originate as very high redshift objects ejected from the nuclei of active galaxies and gradually lose their non-cosmological redshift component as they evolve into galaxies. This stands in stark contradiction to the accepted models of galaxy formation.
The biggest problem with Arp's analysis is that today there are tens of thousands of quasars with known redshifts discovered by various sky surveys. The vast majority of these quasars are not correlated in any way with nearby AGN. Indeed, with improved observing techniques, a number of host galaxies have been observed around quasars which indicates that those quasars at least really are at cosmological distances and are not the kind of objects Arp proposes. Arp's analysis, according to most scientists, suffers from being based on small number statistics and hunting for peculiar coincidences and odd associations. In a vast universe such as our own, peculiarities and oddities are bound to appear if one looks in enough places. Unbiased samples of sources, taken from numerous galaxy surveys of the sky show none of the proposed 'irregularities' nor any statistically significant correlations exist.
In addition, it is not clear what mechanism would be responsible for intrinsic redshifts or their gradual dissipation over time. It is also unclear how nearby quasars would explain some features in the spectrum of quasars which the standard model easily explains. In the standard cosmology, clouds of neutral hydrogen between the quasar and the earth create Lyman alpha absorption lines having different redshifts up to that of the quasar itself; this feature is called the Lyman-alpha forest. Moreover, in extreme quasars one can observe the absorption of neutral hydrogen which has not yet been reionized in a feature known as the Gunn–Peterson trough. Most cosmologists see this missing theoretical work as sufficient reason to explain the observations as either chance or error.
Halton Arp has proposed an explanation for his observations by a Machian "variable mass hypothesis". The variable-mass theory invokes constant matter creation from active galactic nuclei, which puts it into the class of steady-state theories.
Plasma cosmology 
In 1965, Hannes Alfvén proposed a "plasma cosmology" theory of the universe based in part on scaling observations of space plasma physics and experiments on plasmas in terrestrial laboratories to cosmological scales orders-of-magnitude greater. Taking matter–antimatter symmetry as a starting point, Alfvén together with Oskar Klein proposed the Alfvén-Klein cosmology model, based on the fact that since most of the local universe was composed of matter and not antimatter there may be large bubbles of matter and antimatter that would globally balance to equality. The difficulties with this model were apparent almost immediately. Matter–antimatter annihilation results in the production of high energy photons which were not observed. While it was possible that the local "matter-dominated" cell was simply larger than the observable universe, this proposition did not lend itself to observational tests.
Like the steady state theory, plasma cosmology includes a Strong Cosmological Principle which assumes that the universe is isotropic in time as well as in space. Matter is explicitly assumed to have always existed, or at least that it formed at a time so far in the past as to be forever beyond humanity's empirical methods of investigation.
While plasma cosmology has never had the support of most astronomers or physicists, a small number of plasma researchers have continued to promote and develop the approach, and publish in the special issues of the IEEE Transactions on Plasma Science. A few papers regarding plasma cosmology were published in other mainstream journals until the 1990s. Additionally, in 1991, Eric J. Lerner, an independent researcher in plasma physics and nuclear fusion, wrote a popular-level book supporting plasma cosmology called The Big Bang Never Happened. At that time there was renewed interest in the subject among the cosmological community along with other non-standard cosmologies. This was due to anomalous results reported in 1987 by Andrew Lange and Paul Richardson of UC Berkeley and Toshio Matsumoto of Nagoya University that indicated the cosmic microwave background might not have a blackbody spectrum. However, the final announcement (in April 1992) of COBE satellite data corrected the earlier contradiction of the Big Bang; the popularity of plasma cosmology has since fallen.
Nucleosynthesis objections to non-standard cosmologies 
One of the major successes of the Big Bang theory has been to provide a prediction that corresponds to the observations of the abundance of light elements in the universe. Along with the explanation provided for the Hubble's law and for the cosmic microwave background, this observation has proved very difficult for alternative theories to explain.
Theories which assert that the universe has an infinite age, including many of the theories described above, fail to account for the abundance of deuterium in the cosmos, because deuterium easily undergoes nuclear fusion in stars and there are no known astrophysical processes other than the Big Bang itself that can produce it in large quantities. Hence the fact that deuterium is not an extremely rare component of the universe suggests that the universe has a finite age.
Theories which assert that the universe has a finite life, but that the Big Bang did not happen, have problems with the abundance of helium-4. The observed amount of 4He is far larger than the amount that should have been created via stars or any other known process. By contrast, the abundance of 4He in Big Bang models is very insensitive to assumptions about baryon density, changing only a few percent as the baryon density changes by several orders of magnitude. The observed value of 4He is within the range calculated.
- An Open Letter to the Scientific Community
- In the 1990s a contest was held by Sky & Telescope magazine to rename the Big Bang theory and thousands of proposals were offered. The judges concluded that none were any better than the current name.
- See criticism here
- Arp and others who agree with him have been known to support the argument for a varying non-cosmological redshift by referring to a so-called "magnitude-redshift discrepancy". When a Hubble's law-type plot of quasar magnitudes versus redshift is made, a graph with a diffuse scatter and no clear linear relation is generated. However, since absolute magnitudes can only be independently calibrated to an upper limit using size constraints from variability and an Eddington luminosity, it is likely that quasars are exhibiting differing luminosities that cannot necessarily be derived from such simplistic first principles. Arp, Burbidge, and others maintain that the scatter in these plots further supports the idea that quasars have a non-cosmological component to their redshift, but nearly everyone else in the field accepts that quasars have variable luminosity.
- The first instance of observing the host galaxies around quasars was announced in 1983 by Gehren as published in the Proceedings of the Twenty-fourth Liege International Astrophysical Colloquium. p. 489-493.
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