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In cosmology, the steady-state model or steady state theory is an alternative to the Big Bang theory. In the steady-state model, the density of matter in the expanding universe remains unchanged due to a continuous creation of matter, thus adhering to the perfect cosmological principle, a principle that says that the observable universe is always the same at any time and any place.

From the 1940s to the 1960s, the astrophysical community was divided between supporters of the Big Bang theory and supporters of the steady-state theory. The steady-state model is now rejected by most cosmologists, astrophysicists, and astronomers.^[1] The observational evidence points to a hot Big Bang cosmology with a finite age of the universe, which the steady-state model does not predict.^[2]

History

Cosmological expansion was originally seen through observations by Edwin Hubble. Theoretical calculations also showed that the static universe, as modeled by Albert Einstein (1917), was unstable. The modern Big Bang theory, first advanced by Father Georges Lemaître, is one in which the universe has a finite age and has evolved over time through cooling, expansion, and the formation of structures through gravitational collapse.

On the other hand, the steady-state model says while the universe is expanding, it nevertheless does not change its appearance over time (the perfect cosmological principle). E.g., the universe has no beginning and no end. This required that matter be continually created in order to keep the universe's density from decreasing. Influential papers on the topic of a steady-state cosmology were published by Hermann Bondi, Thomas Gold, and Fred Hoyle in 1948.^[3]^[4] Similar models had been proposed earlier by William Duncan MacMillan, among others.^[5]

It is now known that Albert Einstein considered a steady-state model of the expanding universe, as indicated in a 1931 manuscript, many years before Hoyle, Bondi and Gold. However, Einstein abandoned the idea.^[6]

Observational tests

Counts of radio sources

Problems with the steady-state model began to emerge in the 1950s and 60s – observations supported the idea that the universe was in fact changing. Bright radio sources (quasars and radio galaxies) were found only at large distances (therefore could have existed only in the distant past due to the effects of the speed of light on astronomy), not in closer galaxies. Whereas the Big Bang theory predicted as much, the steady-state model predicted that such objects would be found throughout the universe, including close to our own galaxy. By 1961, statistical tests based on radio-source surveys^[7] had ruled out the steady-state model in the minds of most cosmologists, although some proponents of the astronomers like Halton Arp insist that the radio data were suspect.^[1]^: 384

X-ray background

Gold and Hoyle (1959)^[8] considered that matter that is newly created exists in a region that is denser than the average density of the universe. This matter then may radiate and cool faster than the surrounding regions, resulting in a pressure gradient. This gradient would push matter into an over-dense region and result in a thermal instability and emit a large amount of plasma. However, Gould and Burbidge (1963)^[9] realized that the thermal bremsstrahlung radiation emitted by such a plasma would exceed the amount of observed X-rays. Therefore, in the steady-state cosmological model, thermal instability does not appear to be important in the formation of galaxy-sized masses.^[10]

Cosmic microwave background

For most cosmologists, the refutation of the steady-state model came with the discovery of the cosmic microwave background radiation in 1964, which was predicted by the Big Bang theory. The steady-state model explained microwave background radiation as the result of light from ancient stars that has been scattered by galactic dust. However, the cosmic microwave background level is very even in all directions, making it difficult to explain how it could be generated by numerous point sources, and the microwave background radiation shows no evidence of characteristics such as polarization that are normally associated with scattering. Furthermore, its spectrum is so close to that of an ideal black body that it could hardly be formed by the superposition of contributions from a multitude of dust clumps at different temperatures as well as at different redshifts. Steven Weinberg wrote in 1972: "The steady state model does not appear to agree with the observed d_L versus z relation or with source counts ... In a sense, this disagreement is a credit to the model; alone among all cosmologies, the steady state model makes such definite predictions that it can be disproved even with the limited observational evidence at our disposal. The steady state model is so attractive that many of its adherents still retain hope that the evidence against it will eventually disappear as observations improve. However, if the cosmic microwave radiation ... is really black-body radiation, it will be difficult to doubt that the universe has evolved from a hotter denser early stage."^[11]

Since this discovery, the Big Bang theory has been considered to provide the best explanation of the origin of the universe. In most astrophysical publications, the Big Bang is implicitly accepted and is used as the basis of more complete theories.^[12]^: 388

Violations of the cosmological principle

One of the fundamental assumptions of the steady-state model is the cosmological principle, which follows from the perfect cosmological principle and which states that our observational location in the universe is not unusual or special; on a large-enough scale, the universe looks the same in all directions (isotropy) and from every location (homogeneity).^[13] However, recent findings suggest that violations of the cosmological principle, especially of isotropy, exist, with some authors suggesting that the cosmological principle is now obsolete.^[14]^[15]^[16]^[17]

Violations of isotropy

Evidence from galaxy clusters,^[18]^[19] quasars,^[20] and type Ia supernovae^[21] suggests that isotropy is violated on large scales.

Data from the Planck Mission shows hemispheric bias in the cosmic microwave background (CMB) in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies in the CMB are, in fact, statistically significant and can no longer be ignored.^[22]

Already in 1967, Dennis Sciama predicted that the CMB has a significant dipole anisotropy.^[23]^[24] In recent years the CMB dipole has been tested and current results suggest our motion with respect to distant radio galaxies ^[25] and quasars ^[26] differs from our motion with respect to the CMB. The same conclusion has been reached in recent studies of the Hubble diagram of Type Ia supernovae^[27] and quasars.^[28] This contradicts the cosmological principle.

The CMB dipole is hinted at through a number of other observations. First, even within the CMB, there are curious directional alignments ^[29] and an anomalous parity asymmetry ^[30] that may have an origin in the CMB dipole.^[31] Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations,^[32] scaling relations in galaxy clusters,^[33]^[34] strong lensing time delay,^[15] Type Ia supernovae,^[35] and quasars & gamma-ray bursts as standard candles.^[36] The fact that all these independent observables, based on different physics, are tracking the CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole.^{[citation needed]}

Nevertheless, some authors have stated that the universe around Earth is isotropic at high significance by studies of the cosmic microwave background temperature maps.^[37]

Violations of homogeneity

Many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the homogeneity condition required for the cosmological principle, including

The Clowes–Campusano LQG, discovered in 1991, which has a length of 580 Mpc
The Sloan Great Wall, discovered in 2003, which has a length of 423 Mpc,^[38]
U1.11, a large quasar group discovered in 2011, which has a length of 780 Mpc
The Huge-LQG, discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM
The Hercules–Corona Borealis Great Wall, discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)^[39]
The Giant Arc, discovered in June 2021, which has a length of 1000 Mpc^[40]

Other authors claim that the existence of large-scale structures does not necessarily violate the cosmological principle.^[41]^[14]

Quasi-steady state

Quasi-steady-state cosmology (QSS) was proposed in 1993 by Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar as a new incarnation of the steady-state ideas meant to explain additional features unaccounted for in the initial proposal. The model suggests pockets of creation occurring over time within the universe, sometimes referred to as minibangs, mini-creation events, or little bangs.^[42] After the observation of an accelerating universe, further modifications of the model were made.^[43] The Planck particle is a hypothetical black hole whose Schwarzschild radius is approximately the same as its Compton wavelength; the evaporation of such a particle has been evoked as the source of light elements in an expanding steady-state universe.^[44]

Astrophysicist and cosmologist Ned Wright has pointed out flaws in the model.^[45] These first comments were soon rebutted by the proponents.^[46] Wright and other mainstream cosmologists reviewing QSS have pointed out new flaws and discrepancies with observations left unexplained by proponents.^[47]

References

^ ^a ^b Kragh, Helge (1999). Cosmology and Controversy: The Historical Development of Two Theories of the Universe. Princeton University Press. ISBN 978-0-691-02623-7.
^ "Steady State theory". BBC. Retrieved January 11, 2015. [T]he Steady State theorists' ideas are largely discredited today...
^ Bondi, Hermann; Gold, Thomas (1948). "The Steady-State Theory of the Expanding Universe". Monthly Notices of the Royal Astronomical Society. 108 (3): 252. Bibcode:1948MNRAS.108..252B. doi:10.1093/mnras/108.3.252.
^ Hoyle, Fred (1948). "A New Model for the Expanding Universe". Monthly Notices of the Royal Astronomical Society. 108 (5): 372. Bibcode:1948MNRAS.108..372H. doi:10.1093/mnras/108.5.372.
^ Kragh, Helge (2019). "Steady-State theory and the cosmological controversy". In Kragh, Helge (ed.). The Oxford handbook of the history of modern cosmology. pp. 161–205. doi:10.1093/oxfordhb/9780198817666.013.5. ISBN 978-0-19-881766-6. the Chicago astronomer William MacMillan not only assumed that stars and galaxies were distributed uniformly throughout infinite space, he also denied 'that the universe as a whole has ever been or ever will be essentially different from what it is today.'
^ Castelvecchi, Davide (2014). "Einstein's lost theory uncovered". Nature. 506 (7489): 418–419. Bibcode:2014Natur.506..418C. doi:10.1038/506418a. PMID 24572403.
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@@ Line 4: / Line 4: @@
 [[File:Big Bang and Steady-State Theory.png|thumb|In the ''[[Big Bang]]'', the expanding Universe causes matter to dilute over time, while in the Steady-State Theory, continued matter creation ensures that the density remains constant over time.|373x373px]]
-In [[physical cosmology|cosmology]], the '''steady-state model''', or '''steady state theory''' is an alternative to the [[Big Bang]] theory of evolution of the universe. In the steady-state model, the density of matter in the [[expanding universe]] remains unchanged due to a continuous creation of matter,  thus adhering to the [[perfect cosmological principle]], a principle that asserts that the [[observable universe]] is practically the same at any time and any place.
+In [[physical cosmology|cosmology]], the '''steady-state model''' or '''steady state theory''' is an alternative to the [[Big Bang]] theory. In the steady-state model, the density of matter in the [[expanding universe]] remains unchanged due to a continuous creation of matter,  thus adhering to the [[perfect cosmological principle]], a principle that says that the [[observable universe]] is always the same at any time and any place.
-While from the 1940s to the 1960s the astrophysical community was equally divided between supporters of the Big Bang theory and supporters of the steady-state theory, it is now rejected by the vast majority of [[cosmologists]], [[astrophysicists]] and [[astronomers]], as the observational evidence points to a hot Big Bang cosmology with a finite [[age of the universe]], which the steady-state model does not predict.<ref>{{cite web |url=http://www.bbc.co.uk/science/space/universe/questions_and_ideas/steady_state_theory |title=Steady State theory |work=BBC |quote=[T]he Steady State theorists' ideas are largely discredited today... |access-date=January 11, 2015}}</ref><ref name="name">{{cite book |title=Cosmology and Controversy: The Historical Development of Two Theories of the Universe |first=Helge |last=Kragh |authorlink=Helge Kragh |publisher=[[Princeton University Press]] |year=1999 |isbn=978-0-691-02623-7 |url={{Google books |plainurl=yes |id=eq7TfxZOzSEC |page= }} }}</ref>
+From the 1940s to the 1960s, the astrophysical community was divided between supporters of the Big Bang theory and supporters of the steady-state theory. The steady-state model is now rejected by most [[cosmologists]], [[astrophysicists]], and [[astronomers]].<ref name="KraghControversyChapter7">{{cite book |title=Cosmology and Controversy: The Historical Development of Two Theories of the Universe |first=Helge |last=Kragh |author-link=Helge Kragh |publisher=[[Princeton University Press]] |year=1999 |isbn=978-0-691-02623-7 |url={{Google books |plainurl=yes |id=eq7TfxZOzSEC |page= }} }}</ref>
+The observational evidence points to a hot Big Bang cosmology with a finite [[age of the universe]], which the steady-state model does not predict.<ref>{{cite web |url=http://www.bbc.co.uk/science/space/universe/questions_and_ideas/steady_state_theory |title=Steady State theory |work=BBC |quote=[T]he Steady State theorists' ideas are largely discredited today... |access-date=January 11, 2015}}</ref>
 ==History==
+Cosmological expansion was originally seen through observations by [[Edwin Hubble]]. Theoretical calculations also showed that the [[static universe]], as modeled by [[Albert Einstein]] (1917), was unstable. The modern Big Bang theory, first advanced by Father [[Georges Lemaître]], is one in which the universe has a finite age and has evolved over time through cooling, expansion, and the formation of structures through gravitational collapse.
+On the other hand, the steady-state model says while the universe is expanding, it nevertheless does not change its appearance over time (the [[perfect cosmological principle]]). E.g., the universe has no beginning and no end. This required that matter be continually created in order to keep the universe's density from decreasing. Influential papers on the topic of a steady-state cosmology were published by [[Hermann Bondi]], [[Thomas Gold]], and [[Fred Hoyle]] in 1948.<ref>{{cite journal |last1=Bondi |first1=Hermann |last2=Gold |first2=Thomas |title=The Steady-State Theory of the Expanding Universe |journal=Monthly Notices of the Royal Astronomical Society |volume=108 |date=1948 |issue=3 |page=252 |doi=10.1093/mnras/108.3.252 |bibcode=1948MNRAS.108..252B|doi-access=free }}</ref><ref>{{cite journal |last=Hoyle |first=Fred |title=A New Model for the Expanding Universe |journal=Monthly Notices of the Royal Astronomical Society |volume=108 |date=1948 |issue=5 |page=372 |doi=10.1093/mnras/108.5.372 |bibcode=1948MNRAS.108..372H|doi-access=free }}</ref> Similar models had been proposed earlier by [[William Duncan MacMillan]], among others.<ref>{{cite book |editor1-last=Kragh |editor1-first=Helge |date=2019 |title=The Oxford handbook of the history of modern cosmology |isbn=978-0-19-881766-6 |first=Helge |last=Kragh |author-link=Helge Kragh |chapter=Steady-State theory and the cosmological controversy |pages=161–205 |doi=10.1093/oxfordhb/9780198817666.013.5 |quote=the Chicago astronomer William MacMillan not only assumed that stars and galaxies were distributed uniformly throughout infinite space, he also denied 'that the universe as a whole has ever been or ever will be essentially different from what it is today.'}}</ref>
-In the 13th century, [[Siger of Brabant]] authored the thesis ''The Eternity of the World'', which argued that there was no first man, and no first specimen of any particular: the physical universe is thus without any first beginning, and therefore eternal. Siger's views were [[Condemnations of 1210–1277|condemned by the pope in 1277]].
+It is now known that Albert Einstein considered a steady-state model of the expanding universe, as indicated in a 1931 manuscript, many years before Hoyle, Bondi and Gold. However, Einstein abandoned the idea.<ref>{{cite journal |title=Einstein's lost theory uncovered |volume=506 |issue=7489 |pages=418–419 |journal=Nature |bibcode=2014Natur.506..418C |last1=Castelvecchi |first1=Davide |year=2014 |doi=10.1038/506418a|pmid=24572403|doi-access=free}}</ref>
-Cosmological expansion was originally discovered through observations by [[Edwin Hubble]]. Theoretical calculations also showed that the [[static universe]] as modeled by Einstein (1917) was unstable. The modern Big Bang theory, first advanced by Father [[Georges Lemaître]], is one in which the universe has a finite age and has evolved over time through cooling, expansion, and the formation of structures through gravitational collapse.
-The steady-state model asserts that although the universe is expanding, it nevertheless does not change its appearance over time (the [[perfect cosmological principle]]); the universe has no beginning and no end. This required that matter be continually created in order to keep the universe's density from decreasing. Influential papers on steady-state cosmologies were published by [[Hermann Bondi]], [[Thomas Gold]], and [[Fred Hoyle]] in 1948.<ref>{{cite journal |last1=Bondi |first1=Hermann |last2=Gold |first2=Thomas |title=The Steady-State Theory of the Expanding Universe |journal=Monthly Notices of the Royal Astronomical Society |volume=108 |date=1948 |issue=3 |page=252 |doi=10.1093/mnras/108.3.252 |bibcode=1948MNRAS.108..252B|doi-access=free }}</ref><ref>{{cite journal |last=Hoyle |first=Fred |title=A New Model for the Expanding Universe |journal=Monthly Notices of the Royal Astronomical Society |volume=108 |date=1948 |issue=5 |page=372 |doi=10.1093/mnras/108.5.372 |bibcode=1948MNRAS.108..372H|doi-access=free }}</ref> Similar models had been proposed earlier by [[William Duncan MacMillan]], among others.<ref>{{cite book |editor1-last=Kragh |editor1-first=Helge |date=2019 |title=The Oxford handbook of the history of modern cosmology |isbn=978-0-19-881766-6 |first=Helge |last=Kragh |authorlink=Helge Kragh |chapter=Steady-State theory and the cosmological controversy |pages=161–205 |doi=10.1093/oxfordhb/9780198817666.013.5 |quote=the Chicago astronomer William MacMillan not only assumed that stars and galaxies were distributed uniformly throughout infinite space, he also denied 'that the universe as a whole has ever been or ever will be essentially different from what it is today.'}}</ref>
-It is now known that [[Albert Einstein]] considered a steady-state model of the expanding universe, as indicated in a 1931 manuscript, many years before Hoyle, Bondi and Gold. However, Einstein quickly abandoned the idea.<ref>{{cite journal |title=Einstein's lost theory uncovered |volume=506 |issue=7489 |pages=418–419 |journal=Nature |bibcode=2014Natur.506..418C |last1=Castelvecchi |first1=Davide |year=2014 |doi=10.1038/506418a|pmid=24572403|doi-access=free}}</ref>
 ==Observational tests==
 ===Counts of radio sources===
 {{See also|Source counts}}
-Problems with the steady-state model began to emerge in the 1950s and 60s, when observations began to support the idea that the universe was in fact changing: bright radio sources ([[quasar]]s and [[radio galaxy|radio galaxies]]) were found only at large distances (therefore could have existed only in the distant past due to the effects of the [[speed of light]] on astronomy), not in closer galaxies.  Whereas the Big Bang theory predicted as much, the steady-state model predicted that such objects would be found throughout the universe, including close to our own galaxy. By 1961, statistical tests based on radio-source surveys<ref>Ryle and Clarke, "An examination of the steady-state model in the light of some recent observations of radio sources," MNRAW 122 (1961) 349</ref> had ruled out the steady-state model in the minds of most cosmologists, although some proponents of the steady state insisted that the radio data were suspect.
+Problems with the steady-state model began to emerge in the 1950s and 60s – observations supported the idea that the universe was in fact changing. Bright radio sources ([[quasar]]s and [[radio galaxy|radio galaxies]]) were found only at large distances (therefore could have existed only in the distant past due to the effects of the [[speed of light]] on astronomy), not in closer galaxies.  Whereas the Big Bang theory predicted as much, the steady-state model predicted that such objects would be found throughout the universe, including close to our own galaxy. By 1961, statistical tests based on radio-source surveys<ref>Ryle and Clarke, "An examination of the steady-state model in the light of some recent observations of radio sources," MNRAW 122 (1961) 349</ref> had ruled out the steady-state model in the minds of most cosmologists, although some proponents of the astronomers like [[Halton Arp]] insist that the radio data were suspect.<ref name=KraghControversyChapter7/>{{rp|384}}
+===X-ray background===
+Gold and Hoyle (1959)<ref>{{cite journal |last1=Gold |first1=T. |last2=Hoyle |first2=F. |title=Cosmic rays and radio waves as manifestations of a hot universe |journal=Ursi Symp. 1: Paris Symposium on Radio Astronomy |date=1 January 1959 |volume=9 |issue=9 |pages=583 |bibcode=1959IAUS....9..583G |url=https://ui.adsabs.harvard.edu/abs/1959IAUS....9..583G}}</ref>
+considered that matter that is newly created exists in a region that is denser than the average density of the universe. This matter then may radiate and cool faster than the surrounding regions, resulting in a pressure gradient. This gradient would push matter into an over-dense region and result in a thermal instability and emit a large amount of plasma. However, Gould and Burbidge (1963)<ref>{{cite journal |last1=Gould |first1=R. J. |last2=Burbidge |first2=G. R. |title=X-Rays from the Galactic Center, External Galaxies, and the Intergalactic Medium. |journal=The Astrophysical Journal |date=1 November 1963 |volume=138 |pages=969 |doi=10.1086/147698 |bibcode=1963ApJ...138..969G |url=https://ui.adsabs.harvard.edu/abs/1963ApJ...138..969G |issn=0004-637X}}</ref>
+realized that the thermal [[Bremsstrahlung|bremsstrahlung]] radiation emitted by such a plasma would exceed the amount of observed [[X-ray|X-rays]]. Therefore, in the steady-state cosmological model, thermal instability does not appear to be important in the formation of galaxy-sized masses.<ref>{{cite book |last1=Peebles |first1=P. J. E. |title=Cosmology's century: an inside history of our modern understanding of the universe |date=2022 |publisher=Princeton University Press |location=Princeton Oxford |isbn=9780691196022}}</ref>
 ===Cosmic microwave background===
-For most cosmologists, the definitive refutation of the steady-state model came with the discovery of the [[cosmic microwave background]] radiation in 1964, which was predicted by the Big Bang theory. The steady-state model explained microwave background radiation as the result of light from ancient stars that has been scattered by galactic dust.  However, the cosmic microwave background level is very even in all directions, making it difficult to explain how it could be generated by numerous point sources, and the microwave background radiation shows no evidence of characteristics such as polarization that are normally associated with scattering. Furthermore, its spectrum is so close to that of an ideal [[black body]] that it could hardly be formed by the superposition of contributions from a multitude of dust clumps at different temperatures as well as at different [[redshift]]s. [[Steven Weinberg]] wrote in 1972,
+For most cosmologists, the refutation of the steady-state model came with the discovery of the [[cosmic microwave background]] radiation in 1964, which was predicted by the Big Bang theory. The steady-state model explained microwave background radiation as the result of light from ancient stars that has been scattered by galactic dust.  However, the cosmic microwave background level is very even in all directions, making it difficult to explain how it could be generated by numerous point sources, and the microwave background radiation shows no evidence of characteristics such as polarization that are normally associated with scattering. Furthermore, its spectrum is so close to that of an ideal [[black body]] that it could hardly be formed by the superposition of contributions from a multitude of dust clumps at different temperatures as well as at different [[redshift]]s. [[Steven Weinberg]] wrote in 1972: "The steady state model does not appear to agree with the observed [[luminosity distance|d<sub>L</sub>]] versus [[redshift|z]] relation or with [[source counts]] ... In a sense, this disagreement is a credit to the model; alone among all cosmologies, the steady state model makes such definite predictions that it [[falsifiability|can be disproved]] even with the limited observational evidence at our disposal. The steady state model is so attractive that many of its adherents still retain hope that the evidence against it will eventually disappear as observations improve. However, if the cosmic microwave radiation ... is really black-body radiation, it will be difficult to doubt that the universe has evolved from a hotter denser early stage."<ref>{{cite book |last = Weinberg |first = Steven |year = 1972 |title = Gravitation and Cosmology |publisher = John Whitney & Sons |pages = [https://archive.org/details/gravitationcosmo00stev_0/page/463 463–464] |isbn = 978-0-471-92567-5 |url-access = registration |url = https://archive.org/details/gravitationcosmo00stev_0/page/463}}</ref>
-:The steady state model does not appear to agree with the observed [[luminosity distance|d<sub>L</sub>]] versus [[redshift|z]] relation or with [[source counts]] ... In a sense, this disagreement is a credit to the model; alone among all cosmologies, the steady state model makes such definite predictions that it [[falsifiability|can be disproved]] even with the limited observational evidence at our disposal. The steady state model is so attractive that many of its adherents still retain hope that the evidence against it will eventually disappear as observations improve. However, if the cosmic microwave radiation ... is really black-body radiation, it will be difficult to doubt that the universe has evolved from a hotter denser early stage.<ref>
-{{cite book
- |last = Weinberg
- |first = S.
- |year = 1972
- |title = Gravitation and Cosmology
- |publisher = John Whitney & Sons
- |pages = [https://archive.org/details/gravitationcosmo00stev_0/page/495 495–464]
- |isbn = 978-0-471-92567-5
- |url-access = registration
- |url = https://archive.org/details/gravitationcosmo00stev_0/page/495
- }}</ref>
-Since this discovery, the Big Bang theory has been considered to provide the best explanation of the origin of the universe. In most [[astrophysical]] publications, the Big Bang is implicitly accepted and is used as the basis of more complete theories.
+Since this discovery, the Big Bang theory has been considered to provide the best explanation of the origin of the universe. In most [[astrophysical]] publications, the Big Bang is implicitly accepted and is used as the basis of more complete theories.<ref>{{Cite book |last=Kragh |first=Helge |author-link=Helge Kragh |url=https://www.degruyter.com/document/doi/10.1515/9780691227719-008/html |title=Cosmology and Controversy |date=1996-12-31 |publisher=Princeton University Press |isbn=978-0-691-22771-9 |pages=318–388 |chapter=Chapter 7: From Controversy to Marginalization |doi=10.1515/9780691227719-008}}</ref>{{rp|388|q=. What we can say, and should say, is that no developments in science since 1970 have been of such a nature that they have seriously induced scientists to reconsider the basic elements of big-bang cosmology.}}
 ===Violations of the cosmological principle===
 {{main|Cosmological principle|Perfect cosmological principle}}
-One of the fundamental assumptions of the steady-state model is the [[cosmological principle]], which follows from the [[perfect cosmological principle]] and which states that our observational location in the universe is not unusual or special; on a large-enough scale, the universe looks the same in all directions ([[isotropy]]) and from every location ([[homogeneity (physics)|homogeneity]]).<ref>Andrew Liddle. ''An Introduction to Modern Cosmology (2nd ed.).'' London: Wiley, 2003.</ref> However, recent findings have suggested that violations of the cosmological principle, especially of isotropy, exist, with some authors suggesting that the cosmological principle is now obsolete.<ref name="Snowmass21">{{citation|author1=Elcio Abdalla|author2=Guillermo Franco Abellán|author3=Amin Aboubrahim|display-authors=2|title=Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies|journal=Journal of High Energy Astrophysics |arxiv=2203.06142v1|date=11 Mar 2022|volume=34 |page=49 |doi=10.1016/j.jheap.2022.04.002 |bibcode=2022JHEAp..34...49A |s2cid=247411131 }}</ref><ref name="FLRW breakdown"/><ref name="Heinesen-MacPherson">{{cite journal|title=Luminosity distance and anisotropic sky-sampling at low redshifts: A numerical relativity study|url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.023525|author1=Asta Heinesen|author2=Hayley J. Macpherson|journal=Physical Review D|volume=104|issue=2|date=15 July 2021|page=023525|arxiv=2103.11918|doi=10.1103/PhysRevD.104.023525|bibcode=2021PhRvD.104b3525M|s2cid=232307363|access-date=25 March 2022}}</ref><ref name="Colin et al">{{cite journal|title=Evidence for anisotropy of cosmic acceleration|author1=Jacques Colin|author2=Roya Mohayaee|author3=Mohamed Rameez|author4=Subir Sarkar|journal=Astronomy and Astrophysics|volume=631|doi=10.1051/0004-6361/201936373|arxiv=1808.04597|date=20 November 2019|pages=L13|bibcode=2019A&A...631L..13C|s2cid=208175643|access-date=25 March 2022|url=https://www.aanda.org/articles/aa/full_html/2019/11/aa36373-19/aa36373-19.html}}</ref>
+One of the fundamental assumptions of the steady-state model is the [[cosmological principle]], which follows from the [[perfect cosmological principle]] and which states that our observational location in the universe is not unusual or special; on a large-enough scale, the universe looks the same in all directions ([[isotropy]]) and from every location ([[homogeneity (physics)|homogeneity]]).<ref>Andrew Liddle. ''An Introduction to Modern Cosmology (2nd ed.).'' London: Wiley, 2003.</ref> However, recent findings suggest that violations of the cosmological principle, especially of isotropy, exist, with some authors suggesting that the cosmological principle is now obsolete.<ref name="Snowmass21">{{citation|author1=Elcio Abdalla|author2=Guillermo Franco Abellán|author3=Amin Aboubrahim|display-authors=2|title=Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies|journal=Journal of High Energy Astrophysics |arxiv=2203.06142v1|date=11 Mar 2022|volume=34 |page=49 |doi=10.1016/j.jheap.2022.04.002 |bibcode=2022JHEAp..34...49A |s2cid=247411131 }}</ref><ref name="FLRW breakdown"/><ref name="Heinesen-MacPherson">{{cite journal|title=Luminosity distance and anisotropic sky-sampling at low redshifts: A numerical relativity study|url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.023525|author1=Asta Heinesen|author2=Hayley J. Macpherson|journal=Physical Review D|volume=104|issue=2|date=15 July 2021|page=023525|arxiv=2103.11918|doi=10.1103/PhysRevD.104.023525|bibcode=2021PhRvD.104b3525M|s2cid=232307363|access-date=25 March 2022}}</ref><ref name="Colin et al">{{cite journal|title=Evidence for anisotropy of cosmic acceleration|author1=Jacques Colin|author2=Roya Mohayaee|author3=Mohamed Rameez|author4=Subir Sarkar|journal=Astronomy and Astrophysics|volume=631|doi=10.1051/0004-6361/201936373|arxiv=1808.04597|date=20 November 2019|pages=L13|bibcode=2019A&A...631L..13C|s2cid=208175643|access-date=25 March 2022|url=https://www.aanda.org/articles/aa/full_html/2019/11/aa36373-19/aa36373-19.html}}</ref>
 ====Violations of isotropy====
-Evidence from [[galaxy cluster]]s,<ref>{{cite web|url=https://www.scientificamerican.com/article/do-we-live-in-a-lopsided-universe1/|title=Do We Live in a Lopsided Universe?|author=Lee Billings|website=[[Scientific American]]|date=April 15, 2020|access-date=March 24, 2022}}</ref><ref>{{cite journal|url=https://www.aanda.org/articles/aa/full_html/2020/04/aa36602-19/aa36602-19.html|title=Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX-T scaling relation|author1=Migkas, K.|author2=Schellenberger, G.|author3=Reiprich, T. H.|author4=Pacaud, F.|author5=Ramos-Ceja, M. E.|author6=Lovisari, L.|journal=Astronomy & Astrophysics|volume=636|issue=April 2020|pages=42|doi=10.1051/0004-6361/201936602|date=8 April 2020|arxiv=2004.03305|bibcode=2020A&A...636A..15M|s2cid=215238834|access-date=24 March 2022}}</ref> [[quasar]]s,<ref>{{cite journal|url=https://iopscience.iop.org/article/10.3847/2041-8213/abdd40|title=A Test of the Cosmological Principle with Quasars|author1=Nathan J. Secrest|author2=Sebastian von Hausegger|author3=Mohamed Rameez|author4=Roya Mohayaee|author5=Subir Sarkar|author6=Jacques Colin|journal=The Astrophysical Journal Letters|volume=908|issue=2|doi=10.3847/2041-8213/abdd40|arxiv=2009.14826|date=February 25, 2021|pages=L51|bibcode=2021ApJ...908L..51S|s2cid=222066749|access-date=March 24, 2022}}</ref> and [[type Ia supernova]]e<ref>{{cite journal|url=https://iopscience.iop.org/article/10.1088/0004-637X/810/1/47|title=Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae|author1=B. Javanmardi|author2=C. Porciani|author3=P. Kroupa|author4=J. Pflamm-Altenburg|journal=The Astrophysical Journal Letters|volume=810|issue=1|doi=10.1088/0004-637X/810/1/47|arxiv=1507.07560|date=August 27, 2015|page=47|bibcode=2015ApJ...810...47J|s2cid=54958680|access-date=March 24, 2022}}</ref> suggest that isotropy is violated on large scales.
+Evidence from [[galaxy cluster]]s,<ref>{{cite web|url=https://www.scientificamerican.com/article/do-we-live-in-a-lopsided-universe1/|title=Do We Live in a Lopsided Universe?|author=Lee Billings|website=[[Scientific American]]|date=April 15, 2020|access-date=March 24, 2022}}</ref><ref>{{cite journal|url=https://www.aanda.org/articles/aa/full_html/2020/04/aa36602-19/aa36602-19.html|title=Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX-T scaling relation|author1=Migkas, K.|author2=Schellenberger, G.|author3=Reiprich, T. H.|author4=Pacaud, F.|author5=Ramos-Ceja, M. E.|author6=Lovisari, L.|journal=Astronomy & Astrophysics|volume=636|issue=April 2020|page=42|doi=10.1051/0004-6361/201936602|date=8 April 2020|arxiv=2004.03305|bibcode=2020A&A...636A..15M|s2cid=215238834|access-date=24 March 2022}}</ref> [[quasar]]s,<ref>{{cite journal|title=A Test of the Cosmological Principle with Quasars|author1=Nathan J. Secrest|author2=Sebastian von Hausegger|author3=Mohamed Rameez|author4=Roya Mohayaee|author5=Subir Sarkar|author6=Jacques Colin|journal=The Astrophysical Journal Letters|volume=908|issue=2|doi=10.3847/2041-8213/abdd40|arxiv=2009.14826|date=February 25, 2021|pages=L51|bibcode=2021ApJ...908L..51S|s2cid=222066749|doi-access=free }}</ref> and [[type Ia supernova]]e<ref>{{cite journal|url=https://iopscience.iop.org/article/10.1088/0004-637X/810/1/47|title=Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae|author1=B. Javanmardi|author2=C. Porciani|author3=P. Kroupa|author4=J. Pflamm-Altenburg|journal=The Astrophysical Journal Letters|volume=810|issue=1|doi=10.1088/0004-637X/810/1/47|arxiv=1507.07560|date=August 27, 2015|page=47|bibcode=2015ApJ...810...47J|s2cid=54958680|access-date=March 24, 2022}}</ref> suggests that isotropy is violated on large scales.
-Data from the [[Planck Mission]] shows hemispheric bias in the [[cosmic microwave background]] (CMB) in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The [[European Space Agency]] (the governing body of the Planck Mission) has concluded that these anisotropies in the  CMB are, in fact, statistically significant and can no longer be ignored.<ref name="Planck">{{cite web | url=http://sci.esa.int/planck/51551-simple-but-challenging-the-universe-according-to-planck/ | title=Simple but challenging: the Universe according to Planck | work=[[ESA Science & Technology]] | orig-year=March 21, 2013 |date= October 5, 2016 | access-date=October 29, 2016}}</ref>
+Data from the [[Planck Mission]] shows hemispheric bias in the [[cosmic microwave background]] (CMB) in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The [[European Space Agency]] (the governing body of the Planck Mission) has concluded that these anisotropies in the  CMB are, in fact, statistically significant and can no longer be ignored.<ref name="Planck">{{cite web | url=http://sci.esa.int/planck/51551-simple-but-challenging-the-universe-according-to-planck/ | title=Simple but challenging: the Universe according to Planck | work=[[ESA Science & Technology]] | orig-date=March 21, 2013 |date= October 5, 2016 | access-date=October 29, 2016}}</ref>
-Already in 1967, [[Dennis Sciama]] predicted that the CMB has a significant dipole anisotropy.<ref name="sciama">{{cite journal|title=Peculiar Velocity of the Sun and the Cosmic Microwave Background|url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.18.1065|author=Dennis Sciama|journal=Physical Review Letters|volume=18|issue=24|doi=10.1103/PhysRevLett.18.1065|date=12 June 1967|pages=1065–1067|bibcode=1967PhRvL..18.1065S|access-date=25 March 2022}}</ref><ref>{{cite journal|title=On the expected anisotropy of radio source counts|url=https://academic.oup.com/mnras/article/206/2/377/1024995|author1=G. F. R. Ellis|author2=J. E. Baldwin|journal=Monthly Notices of the Royal Astronomical Society|volume=206|issue=2|doi=10.1093/mnras/206.2.377|date=1 January 1984|pages=377–381|access-date=25 March 2022|doi-access=free}}</ref> In recent years the CMB dipole has been tested and current results suggest our motion with respect to distant radio galaxies <ref>{{cite journal |last1=Siewert |first1=Thilo M. |last2=Schmidt-Rubart |first2=Matthias |last3=Schwarz |first3=Dominik J. |title=Cosmic radio dipole: Estimators and frequency dependence |journal=Astronomy & Astrophysics |year=2021 |volume=653 |pages=A9 |doi=10.1051/0004-6361/202039840 |arxiv=2010.08366|bibcode=2021A&A...653A...9S |s2cid=223953708 }}</ref> and quasars <ref>{{cite journal |last1=Secrest |first1=Nathan |last2=von Hausegger |first2=Sebastian |last3=Rameez |first3=Mohamed |last4=Mohayaee |first4=Roya |last5=Sarkar |first5=Subir |last6=Colin |first6=Jacques |title=A Test of the Cosmological Principle with Quasars |journal=The Astrophysical Journal |date=25 February 2021 |volume=908 |issue=2 |pages=L51 |doi=10.3847/2041-8213/abdd40 |arxiv=2009.14826 |bibcode=2021ApJ...908L..51S |s2cid=222066749 |issn=2041-8213}}</ref> differs from our motion with respect to the CMB. The same conclusion has been reached in recent studies of the [[Hubble diagram]] of [[Type Ia supernovae]]<ref>{{cite journal |last1=Singal |first1=Ashok K. |title=Peculiar motion of Solar system from the Hubble diagram of supernovae Ia and its implications for cosmology |journal=Monthly Notices of the Royal Astronomical Society |year=2022 |volume=515 |issue=4 |pages=5969–5980 |doi=10.1093/mnras/stac1986 |arxiv=2106.11968}}</ref> and [[quasars]].<ref>{{cite journal |last1=Singal |first1=Ashok K. |title=Solar system peculiar motion from the Hubble diagram of quasars and testing the cosmological principle |journal=Monthly Notices of the Royal Astronomical Society |year=2022 |volume=511 |issue=2 |pages=1819–1829 |doi=10.1093/mnras/stac144 |arxiv=2107.09390}}</ref> This contradicts the cosmological principle.
+Already in 1967, [[Dennis Sciama]] predicted that the CMB has a significant dipole anisotropy.<ref name="sciama">{{cite journal|title=Peculiar Velocity of the Sun and the Cosmic Microwave Background|url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.18.1065|author=Dennis Sciama|journal=Physical Review Letters|volume=18|issue=24|doi=10.1103/PhysRevLett.18.1065|date=12 June 1967|pages=1065–1067|bibcode=1967PhRvL..18.1065S|access-date=25 March 2022}}</ref><ref>{{cite journal|title=On the expected anisotropy of radio source counts|url=https://academic.oup.com/mnras/article/206/2/377/1024995|author1=G. F. R. Ellis|author2=J. E. Baldwin|journal=Monthly Notices of the Royal Astronomical Society|volume=206|issue=2|doi=10.1093/mnras/206.2.377|date=1 January 1984|pages=377–381|access-date=25 March 2022|doi-access=free}}</ref> In recent years the CMB dipole has been tested and current results suggest our motion with respect to distant radio galaxies <ref>{{cite journal |last1=Siewert |first1=Thilo M. |last2=Schmidt-Rubart |first2=Matthias |last3=Schwarz |first3=Dominik J. |title=Cosmic radio dipole: Estimators and frequency dependence |journal=Astronomy & Astrophysics |year=2021 |volume=653 |pages=A9 |doi=10.1051/0004-6361/202039840 |arxiv=2010.08366|bibcode=2021A&A...653A...9S |s2cid=223953708 }}</ref> and quasars <ref>{{cite journal |last1=Secrest |first1=Nathan |last2=von Hausegger |first2=Sebastian |last3=Rameez |first3=Mohamed |last4=Mohayaee |first4=Roya |last5=Sarkar |first5=Subir |last6=Colin |first6=Jacques |title=A Test of the Cosmological Principle with Quasars |journal=The Astrophysical Journal |date=25 February 2021 |volume=908 |issue=2 |pages=L51 |doi=10.3847/2041-8213/abdd40 |arxiv=2009.14826 |bibcode=2021ApJ...908L..51S |s2cid=222066749 |issn=2041-8213 |doi-access=free }}</ref> differs from our motion with respect to the CMB. The same conclusion has been reached in recent studies of the [[Hubble diagram]] of [[Type Ia supernovae]]<ref>{{cite journal |last1=Singal |first1=Ashok K. |title=Peculiar motion of Solar system from the Hubble diagram of supernovae Ia and its implications for cosmology |journal=Monthly Notices of the Royal Astronomical Society |year=2022 |volume=515 |issue=4 |pages=5969–5980 |doi=10.1093/mnras/stac1986 |doi-access=free |arxiv=2106.11968}}</ref> and [[quasars]].<ref>{{cite journal |last1=Singal |first1=Ashok K. |title=Solar system peculiar motion from the Hubble diagram of quasars and testing the cosmological principle |journal=Monthly Notices of the Royal Astronomical Society |year=2022 |volume=511 |issue=2 |pages=1819–1829 |doi=10.1093/mnras/stac144 |doi-access=free |arxiv=2107.09390}}</ref> This contradicts the cosmological principle.
-The CMB dipole is hinted at through a number of other observations. First, even within the CMB, there are curious directional alignments <ref>{{cite journal |last1=de Oliveira-Costa |first1=Angelica |last2=Tegmark |first2=Max |last3=Zaldarriaga |first3=Matias |last4=Hamilton |first4=Andrew |title=The significance of the largest scale CMB fluctuations in WMAP |journal=Physical Review D |date=25 March 2004 |volume=69 |issue=6 |pages=063516 |doi=10.1103/PhysRevD.69.063516 |arxiv=astro-ph/0307282 |bibcode=2004PhRvD..69f3516D |s2cid=119463060 |issn=1550-7998}}</ref> and an anomalous parity asymmetry <ref>{{cite journal |last1=Land |first1=Kate |last2=Magueijo |first2=Joao |title=Is the Universe odd? |journal=Physical Review D |date=28 November 2005 |volume=72 |issue=10 |pages=101302 |doi=10.1103/PhysRevD.72.101302 |arxiv=astro-ph/0507289 |bibcode=2005PhRvD..72j1302L |s2cid=119333704 |issn=1550-7998}}</ref> that may have an origin in the CMB dipole.<ref>{{cite journal |last1=Kim |first1=Jaiseung |last2=Naselsky |first2=Pavel |title=Anomalous parity asymmetry of the Wilkinson Microwave Anisotropy Probe power spectrum data at low multipoles |journal=The Astrophysical Journal |date=10 May 2010 |volume=714 |issue=2 |pages=L265–L267 |doi=10.1088/2041-8205/714/2/L265 |arxiv=1001.4613 |bibcode=2010ApJ...714L.265K |s2cid=24389919 |issn=2041-8205}}</ref> Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations,<ref>{{cite journal |last1=Hutsemekers |first1=D. |last2=Cabanac |first2=R. |last3=Lamy |first3=H. |last4=Sluse |first4=D. |title=Mapping extreme-scale alignments of quasar polarization vectors |journal=Astronomy & Astrophysics |date=October 2005 |volume=441 |issue=3 |pages=915–930 |doi=10.1051/0004-6361:20053337 |arxiv=astro-ph/0507274 |bibcode=2005A&A...441..915H |s2cid=14626666 |issn=0004-6361}}</ref> scaling relations in galaxy clusters,<ref>{{cite journal |last1=Migkas |first1=K. |last2=Schellenberger |first2=G. |last3=Reiprich |first3=T. H. |last4=Pacaud |first4=F. |last5=Ramos-Ceja |first5=M. E. |last6=Lovisari |first6=L. |title=Probing cosmic isotropy with a new X-ray galaxy cluster sample through the <math>L_{\text{X}}-T</math> scaling relation |journal=Astronomy & Astrophysics |date=April 2020 |volume=636 |pages=A15 |doi=10.1051/0004-6361/201936602 |arxiv=2004.03305 |bibcode=2020A&A...636A..15M |s2cid=215238834 |issn=0004-6361}}</ref><ref>{{cite journal |last1=Migkas |first1=K. |last2=Pacaud |first2=F. |last3=Schellenberger |first3=G. |last4=Erler |first4=J. |last5=Nguyen-Dang |first5=N. T. |last6=Reiprich |first6=T. H. |last7=Ramos-Ceja |first7=M. E. |last8=Lovisari |first8=L. |title=Cosmological implications of the anisotropy of ten galaxy cluster scaling relations |journal=Astronomy & Astrophysics |date=May 2021 |volume=649 |pages=A151 |doi=10.1051/0004-6361/202140296 |arxiv=2103.13904 |bibcode=2021A&A...649A.151M |s2cid=232352604 |issn=0004-6361}}</ref> [[strong lensing]] time delay,<ref name="FLRW breakdown">{{cite journal |last1=Krishnan |first1=Chethan |last2=Mohayaee |first2=Roya |last3=Colgáin |first3=Eoin Ó |last4=Sheikh-Jabbari |first4=M. M. |last5=Yin |first5=Lu |title=Does Hubble Tension Signal a Breakdown in FLRW Cosmology? |journal=Classical and Quantum Gravity |date=16 September 2021 |volume=38 |issue=18 |pages=184001 |doi=10.1088/1361-6382/ac1a81 |arxiv=2105.09790 |bibcode=2021CQGra..38r4001K |s2cid=234790314 |issn=0264-9381}}</ref> Type Ia supernovae,<ref>{{cite journal |last1=Krishnan |first1=Chethan |last2=Mohayaee |first2=Roya |last3=Colgáin |first3=Eoin Ó |last4=Sheikh-Jabbari |first4=M. M. |last5=Yin |first5=Lu |title=Hints of FLRW breakdown from supernovae |journal=Physical Review D |year=2022 |volume=105 |issue=6 |page=063514 |doi=10.1103/PhysRevD.105.063514 |arxiv=2106.02532|bibcode=2022PhRvD.105f3514K |s2cid=235352881 }}</ref> and quasars & [[gamma-ray bursts]] as [[standard candles]].<ref>{{cite journal |last1=Luongo |first1=Orlando |last2=Muccino |first2=Marco |last3=Colgáin |first3=Eoin Ó |last4=Sheikh-Jabbari |first4=M. M. |last5=Yin |first5=Lu |title=Larger H0 values in the CMB dipole direction |journal=Physical Review D |year=2022 |volume=105 |issue=10 |page=103510 |doi=10.1103/PhysRevD.105.103510 |arxiv=2108.13228|bibcode=2022PhRvD.105j3510L |s2cid=248713777 }}</ref> The fact that all these independent observables, based on different physics, are tracking the CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole.
+The CMB dipole is hinted at through a number of other observations. First, even within the CMB, there are curious directional alignments <ref>{{cite journal |last1=de Oliveira-Costa |first1=Angelica |last2=Tegmark |first2=Max |last3=Zaldarriaga |first3=Matias |last4=Hamilton |first4=Andrew |title=The significance of the largest scale CMB fluctuations in WMAP |journal=Physical Review D |date=25 March 2004 |volume=69 |issue=6 |page=063516 |doi=10.1103/PhysRevD.69.063516 |arxiv=astro-ph/0307282 |bibcode=2004PhRvD..69f3516D |s2cid=119463060 |issn=1550-7998}}</ref> and an anomalous parity asymmetry <ref>{{cite journal |last1=Land |first1=Kate |last2=Magueijo |first2=Joao |title=Is the Universe odd? |journal=Physical Review D |date=28 November 2005 |volume=72 |issue=10 |page=101302 |doi=10.1103/PhysRevD.72.101302 |arxiv=astro-ph/0507289 |bibcode=2005PhRvD..72j1302L |s2cid=119333704 |issn=1550-7998}}</ref> that may have an origin in the CMB dipole.<ref>{{cite journal |last1=Kim |first1=Jaiseung |last2=Naselsky |first2=Pavel |title=Anomalous parity asymmetry of the Wilkinson Microwave Anisotropy Probe power spectrum data at low multipoles |journal=The Astrophysical Journal |date=10 May 2010 |volume=714 |issue=2 |pages=L265–L267 |doi=10.1088/2041-8205/714/2/L265 |arxiv=1001.4613 |bibcode=2010ApJ...714L.265K |s2cid=24389919 |issn=2041-8205}}</ref> Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations,<ref>{{cite journal |last1=Hutsemekers |first1=D. |last2=Cabanac |first2=R. |last3=Lamy |first3=H. |last4=Sluse |first4=D. |title=Mapping extreme-scale alignments of quasar polarization vectors |journal=Astronomy & Astrophysics |date=October 2005 |volume=441 |issue=3 |pages=915–930 |doi=10.1051/0004-6361:20053337 |arxiv=astro-ph/0507274 |bibcode=2005A&A...441..915H |s2cid=14626666 |issn=0004-6361}}</ref> scaling relations in galaxy clusters,<ref>{{cite journal |last1=Migkas |first1=K. |last2=Schellenberger |first2=G. |last3=Reiprich |first3=T. H. |last4=Pacaud |first4=F. |last5=Ramos-Ceja |first5=M. E. |last6=Lovisari |first6=L. |title=Probing cosmic isotropy with a new X-ray galaxy cluster sample through the <math>L_{\text{X}}-T</math> scaling relation |journal=Astronomy & Astrophysics |date=April 2020 |volume=636 |pages=A15 |doi=10.1051/0004-6361/201936602 |arxiv=2004.03305 |bibcode=2020A&A...636A..15M |s2cid=215238834 |issn=0004-6361}}</ref><ref>{{cite journal |last1=Migkas |first1=K. |last2=Pacaud |first2=F. |last3=Schellenberger |first3=G. |last4=Erler |first4=J. |last5=Nguyen-Dang |first5=N. T. |last6=Reiprich |first6=T. H. |last7=Ramos-Ceja |first7=M. E. |last8=Lovisari |first8=L. |title=Cosmological implications of the anisotropy of ten galaxy cluster scaling relations |journal=Astronomy & Astrophysics |date=May 2021 |volume=649 |pages=A151 |doi=10.1051/0004-6361/202140296 |arxiv=2103.13904 |bibcode=2021A&A...649A.151M |s2cid=232352604 |issn=0004-6361}}</ref> [[strong lensing]] time delay,<ref name="FLRW breakdown">{{cite journal |last1=Krishnan |first1=Chethan |last2=Mohayaee |first2=Roya |last3=Colgáin |first3=Eoin Ó |last4=Sheikh-Jabbari |first4=M. M. |last5=Yin |first5=Lu |title=Does Hubble Tension Signal a Breakdown in FLRW Cosmology? |journal=Classical and Quantum Gravity |date=16 September 2021 |volume=38 |issue=18 |page=184001 |doi=10.1088/1361-6382/ac1a81 |arxiv=2105.09790 |bibcode=2021CQGra..38r4001K |s2cid=234790314 |issn=0264-9381}}</ref> Type Ia supernovae,<ref>{{cite journal |last1=Krishnan |first1=Chethan |last2=Mohayaee |first2=Roya |last3=Colgáin |first3=Eoin Ó |last4=Sheikh-Jabbari |first4=M. M. |last5=Yin |first5=Lu |title=Hints of FLRW breakdown from supernovae |journal=Physical Review D |year=2022 |volume=105 |issue=6 |page=063514 |doi=10.1103/PhysRevD.105.063514 |arxiv=2106.02532|bibcode=2022PhRvD.105f3514K |s2cid=235352881 }}</ref> and quasars & [[gamma-ray bursts]] as [[standard candles]].<ref>{{cite journal |last1=Luongo |first1=Orlando |last2=Muccino |first2=Marco |last3=Colgáin |first3=Eoin Ó |last4=Sheikh-Jabbari |first4=M. M. |last5=Yin |first5=Lu |title=Larger H0 values in the CMB dipole direction |journal=Physical Review D |year=2022 |volume=105 |issue=10 |page=103510 |doi=10.1103/PhysRevD.105.103510 |arxiv=2108.13228|bibcode=2022PhRvD.105j3510L |s2cid=248713777 }}</ref> The fact that all these independent observables, based on different physics, are tracking the CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole.{{citation needed|date=February 2024}}
-Nevertheless, some authors have stated that the universe around Earth is isotropic at high significance by studies of the cosmic microwave background temperature maps.<ref name=Saadeh>{{cite journal| vauthors = Saadeh D, Feeney SM, Pontzen A, Peiris HV, McEwen, JD|title=How Isotropic is the Universe?|journal=Physical Review Letters|date=2016|volume=117|number=13|pages= 131302 |doi=10.1103/PhysRevLett.117.131302|pmid=27715088|arxiv=1605.07178|bibcode = 2016PhRvL.117m1302S |s2cid=453412}}</ref>
+Nevertheless, some authors have stated that the universe around Earth is isotropic at high significance by studies of the cosmic microwave background temperature maps.<ref name=Saadeh>{{cite journal| vauthors = Saadeh D, Feeney SM, Pontzen A, Peiris HV, McEwen, JD|title=How Isotropic is the Universe?|journal=Physical Review Letters|date=2016|volume=117|number=13|page= 131302 |doi=10.1103/PhysRevLett.117.131302|pmid=27715088|arxiv=1605.07178|bibcode = 2016PhRvL.117m1302S |s2cid=453412}}</ref>
 ====Violations of homogeneity====
 Many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the homogeneity condition required for the cosmological principle, including
 * The [[Clowes–Campusano LQG]], discovered in 1991, which has a length of 580 Mpc
-* The [[Sloan Great Wall]], discovered in 2003, which has a length of 423 Mpc,<ref name=apj624_2_463>{{Cite journal | display-authors=1 | last1=Gott | first1=J. Richard, III | last2=Jurić | first2=Mario | last3=Schlegel| first3=David | last4=Hoyle | first4=Fiona | last5=Vogeley | first5=Michael | last6=Tegmark | first6=Max | last7=Bahcall | first7=Neta |last8=Brinkmann | first8=Jon | title=A Map of the Universe | journal=The Astrophysical Journal | volume=624 | issue=2 | pages=463–484 |date=May 2005 | doi=10.1086/428890 | bibcode=2005ApJ...624..463G |arxiv = astro-ph/0310571| s2cid=9654355 }}</ref>
+* The [[Sloan Great Wall]], discovered in 2003, which has a length of 423 Mpc,<ref name=apj624_2_463>{{Cite journal | display-authors=1 | last1=Gott | first1=J. Richard III | last2=Jurić | first2=Mario | last3=Schlegel| first3=David | last4=Hoyle | first4=Fiona | last5=Vogeley | first5=Michael | last6=Tegmark | first6=Max | last7=Bahcall | first7=Neta |last8=Brinkmann | first8=Jon | title=A Map of the Universe | journal=The Astrophysical Journal | volume=624 | issue=2 | pages=463–484 |date=May 2005 | doi=10.1086/428890 | bibcode=2005ApJ...624..463G |arxiv = astro-ph/0310571| s2cid=9654355 }}</ref>
 * [[U1.11]], a [[large quasar group]] discovered in 2011, which has a length of 780 Mpc
 * The [[Huge-LQG]], discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM
 * The [[Hercules–Corona Borealis Great Wall]], discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)<ref>{{cite arXiv |eprint=1311.1104|last1= Horvath|first1= I.|title= The largest structure of the Universe, defined by Gamma-Ray Bursts|last2=  Hakkila|first2= J.|last3=  Bagoly|first3= Z.|class= astro-ph.CO|year= 2013}}</ref>
-*The [[The Giant Arc|Giant Arc]], discovered in June 2021, which has a length of 1000 Mpc<ref>{{Cite web|url=https://www.newscientist.com/article/2280076-line-of-galaxies-is-so-big-it-breaks-our-understanding-of-the-universe/|title = Line of galaxies is so big it breaks our understanding of the universe}}</ref>
+* The [[The Giant Arc|Giant Arc]], discovered in June 2021, which has a length of 1000 Mpc<ref>{{Cite web|url=https://www.newscientist.com/article/2280076-line-of-galaxies-is-so-big-it-breaks-our-understanding-of-the-universe/|title = Line of galaxies is so big it breaks our understanding of the universe}}</ref>
-Other authors claim that the existence of large-scale structures does not necessarily violate the cosmological principle.<ref name=Nadathur>{{cite journal|last=Nadathur|first=Seshadri|title=Seeing patterns in noise: gigaparsec-scale 'structures' that do not violate homogeneity|journal=Monthly Notices of the Royal Astronomical Society|date=2013|volume=434|issue=1|pages=398–406|doi=10.1093/mnras/stt1028|arxiv=1306.1700|bibcode =2013MNRAS.434..398N|s2cid=119220579}}</ref><ref name="Snowmass21"/>
+Other authors claim that the existence of large-scale structures does not necessarily violate the cosmological principle.<ref name=Nadathur>{{cite journal|last=Nadathur|first=Seshadri|title=Seeing patterns in noise: gigaparsec-scale 'structures' that do not violate homogeneity|journal=Monthly Notices of the Royal Astronomical Society|date=2013|volume=434|issue=1|pages=398–406|doi=10.1093/mnras/stt1028|doi-access=free |arxiv=1306.1700|bibcode =2013MNRAS.434..398N|s2cid=119220579}}</ref><ref name="Snowmass21"/>
 ==Quasi-steady state==
@@ Line 78: / Line 69: @@
  |bibcode=1993ApJ...410..437H
  |doi=10.1086/172761
+|doi-access=free
-}}<br />
+ }}<br />
 {{cite journal
  |last1=Hoyle |first1=F.
@@ Line 89: / Line 81: @@
  |pages=1007–1019
  |bibcode=1994MNRAS.267.1007H
  |doi=10.1093/mnras/267.4.1007
 |hdl=11007/1133|doi-access=free
  }}<br />
@@ Line 97: / Line 89: @@
  |last3=Narlikar |first3=J. V.
  |year=1994
- |title=Astrophysical deductions from the quasi-steady state : Erratum
+ |title=Astrophysical deductions from the quasi-steady state: Erratum
  |journal=[[Monthly Notices of the Royal Astronomical Society]]
  |volume=269 |issue=4
  |page=1152
  |bibcode=1994MNRAS.269.1152H
  |doi=10.1093/mnras/269.4.1152
 |doi-access=free
  }}<br />
@@ Line 157: / Line 149: @@
 |volume=276
  |issue=4
- |pages=1421
+ |page=1421
+ |doi-access=free
  |bibcode = 1995MNRAS.276.1421W |s2cid=118904109
  }}
@@ Line 180: / Line 173: @@
 ==See also==
 * [[Non-standard cosmology]]
-* [[Background independence]]
 * [[Copernican principle]]
-* [[End of Greatness]]
+* [[Large-scale structure of the cosmos]]
-* [[Large scale structure of the cosmos]]
+* [[Expansion of the universe]]
-* [[Metric expansion of space]]
+==References==
-==Notes and citations==
 <!-- The other references need to be converted to inline references. -->
 {{reflist|40em}}
 ==Further reading==
-* [http://casswww.ucsd.edu/archive/personal/burbidge/pubs/985623.pdf Burbidge, G., Hoyle, F., "The Origin of Helium and the Other Light Elements", ''The Astrophysical Journal'', 509:L1–L3, 10 December 1998]
+* [http://casswww.ucsd.edu/archive/personal/burbidge/pubs/985623.pdf Burbidge, G., Hoyle, F., "The Origin of Helium and the Other Light Elements", ''The Astrophysical Journal'', 509: L1–L3, 10 December 1998]
-*{{cite book
+* {{cite book
  |last1=Hoyle |first1=F.
  |last2=Burbidge |first2=G.
@@ Line 201: / Line 192: @@
  |isbn=978-0-521-66223-9
 }}
-*{{cite book
+* {{cite book
  |last=Mitton |first=S.
  |year=2005
@@ Line 208: / Line 199: @@
  |isbn=978-0-309-09313-2
 }}
-*{{cite book
+* {{cite book
  |last=Mitton |first=S.
  |year=2005
@@ Line 215: / Line 206: @@
  |isbn=978-1-85410-961-3
 }}
-*{{cite book
+* {{cite book
  |last1=Narlikar |first1=Jayant
  |last2=Burbidge |first2=Geoffrey
  |year=2008
  |title=Facts and Speculations in Cosmology
  |publisher=[[Cambridge University Press]]
- |isbn=978-0521865043
+ |isbn=978-0-521-86504-3
 }}
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