Editing Lambda-CDM model (section)

=== Violations of the cosmological principle ===
{{main|Cosmological principle|Friedmann–Lemaître–Robertson–Walker metric}}
The ΛCDM model, like all models built on the Friedmann–Lemaître–Robertson–Walker metric, assume that the universe looks the same in all directions ([[isotropy]]) and from every location ([[homogeneity (physics)|homogeneity]]) on a large enough scale: "the universe looks the same whoever and wherever you are."<ref>Andrew Liddle. ''An Introduction to Modern Cosmology (2nd ed.).'' London: Wiley, 2003.</ref> This [[cosmological principle]] allows a metric, [[Friedmann–Lemaître–Robertson–Walker metric]], to be derived and developed into a theory to compare to experiments. Without the principle, a metric would need to be extracted from astronomical data, which may not be possible.<ref>{{cite book|title=Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity|author=[[Steven Weinberg]]|isbn=978-0-471-92567-5|year=1972|publisher=John Wiley & Sons, Inc.}}</ref>{{rp|408}} The assumptions were carried over into the ΛCDM model.<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> However, some findings suggested violations of the cosmological principle.<ref name="Snowmass21"/><ref name="FLRW breakdown"/>

==== 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|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> suggest that isotropy is violated on large scales.{{citation needed|date=February 2024}}

Data from the [[Planck Mission]] shows hemispheric bias in the [[cosmic microwave background]] 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 cosmic microwave background 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|url-access=subscription}}</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 the 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 [[cosmic microwave background]]. 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.{{citation needed|date=February 2024}}

The CMB dipole is hinted at through a number of other observations. First, even within the cosmic microwave background, 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 and [[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 combined cosmic microwave background temperature and polarization 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 ====
The homogeneity of the universe needed for the ΛCDM applies to very large volumes of space.
[[N-body simulation]]s in ΛCDM show that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260[[Parsec#Megaparsecs and gigaparsecs|/h Mpc]] or more.<ref name=Yadav>{{cite journal|last=Yadav|first=Jaswant |author2=J. S. Bagla |author3=Nishikanta Khandai|title=Fractal dimension as a measure of the scale of homogeneity|journal=Monthly Notices of the Royal Astronomical Society|date=25 February 2010|volume=405|issue=3|pages=2009–2015|doi=10.1111/j.1365-2966.2010.16612.x |doi-access=free |arxiv = 1001.0617 |bibcode = 2010MNRAS.405.2009Y |s2cid=118603499 }}</ref> 
Numerous claims of large-scale structures reported to be in conflict with the predicted scale of homogeneity for ΛCDM do not withstand statistical analysis.<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"/>{{rp|7.8}}