Editing Lambda-CDM model (section)

== Challenges ==
Despite the widespread success of ΛCDM in matching observations of our universe, cosmologists believe that the model may be an approximation of a more fundamental model.<ref name="Snowmass21">{{cite journal|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="cern-courier">{{cite web|url=https://cerncourier.com/a/exploring-the-hubble-tension/|title=Exploring the Hubble tension|author=Matthew Chalmers|website=[[CERN Courier]]|date=2 July 2021|access-date=25 March 2022}}</ref><ref name="Turner">{{cite journal|author1=Michael Turner|title=The Road to Precision Cosmology|journal=Annual Review of Nuclear and Particle Science|volume=32|arxiv=2201.04741|date=12 Jan 2022|pages=1–35 |doi=10.1146/annurev-nucl-111119-041046|bibcode=2022ARNPS..72....1T |s2cid=245906450 }}</ref>

=== Lack of detection ===
Extensive searches for dark matter particles have so far shown no well-agreed detection, while dark energy may be almost impossible to detect in a laboratory, and its value is [[cosmological constant problem|extremely small]] compared to [[Vacuum energy|vacuum energy theoretical predictions]].{{citation needed|date=February 2024}}

=== 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}}

=== El Gordo galaxy cluster collision ===
{{main|El Gordo (galaxy cluster)}}

[[El Gordo (galaxy cluster)|El Gordo]] is a massive interacting galaxy cluster in the early Universe (<math>z = 0.87</math>). The extreme properties of [[El Gordo (galaxy cluster)|El Gordo]] in terms of its redshift, mass, and the collision velocity leads to strong (<math>6.16\sigma</math>) tension with the ΛCDM model.<ref name="Asencio">{{Cite journal|last1=Asencio|first1=E|last2=Banik|first2=I|last3=Kroupa|first3=P|date=2021-02-21|title=A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology|journal=Monthly Notices of the Royal Astronomical Society|volume=500|issue=2|pages=5249–5267|doi=10.1093/mnras/staa3441|arxiv=2012.03950|bibcode=2021MNRAS.500.5249A|issn=0035-8711|doi-access=free}}</ref><ref name="Asencio_2023">{{Cite journal|last1=Asencio|first1=E|last2=Banik|first2=I|last3=Kroupa|first3=P|date=2023-09-10|title=A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology|journal=The Astrophysical Journal|volume=954|issue=2|pages=162|doi=10.3847/1538-4357/ace62a|doi-access=free|arxiv=2308.00744|bibcode=2023ApJ...954..162A|issn=1538-4357}}</ref> The properties of [[El Gordo (galaxy cluster)|El Gordo]] are however consistent with cosmological simulations in the framework of [[MOND]] due to more rapid structure formation.<ref name="Katz">{{Cite journal|last1=Katz|first1=H|last2=McGaugh|first2=S|last3=Teuben|first3=P|last4=Angus|first4=G. W.|date=2013-07-20|title=Galaxy Cluster Bulk Flows and Collision Velocities in QUMOND|journal = The Astrophysical Journal|volume=772|issue=1|page=10|doi=10.1088/0004-637X/772/1/10|arxiv=1305.3651|bibcode=2013ApJ...772...10K|issn=1538-4357|doi-access=free}}</ref>

=== KBC void ===
{{main|KBC void}}

The [[KBC void]] is an immense, comparatively empty region of space containing the [[Milky Way]] approximately 2 billion light-years (600 megaparsecs, Mpc) in diameter.<ref name="kbc">{{Cite journal | last1 = Keenan | first1 = Ryan C. | last2 = Barger | first2 = Amy J. | last3 = Cowie | first3 = Lennox L. | title = Evidence for a ~300&nbsp;Mpc Scale Under-density in the Local Galaxy Distribution | journal = The Astrophysical Journal | volume = 775 | year = 2013 | issue = 1 | page = 62 | doi = 10.1088/0004-637X/775/1/62 |arxiv = 1304.2884 |bibcode = 2013ApJ...775...62K | s2cid = 118433293 }}</ref><ref name="siegel">{{cite web|url=https://www.forbes.com/sites/startswithabang/2017/06/07/were-way-below-average-astronomers-say-milky-way-resides-in-a-great-cosmic-void/#4d53c7cd6d05|title=We're Way Below Average! Astronomers Say Milky Way Resides In A Great Cosmic Void|last=Siegel|first=Ethan|work=[[Forbes]]|access-date=2017-06-09}}</ref><ref name="Snowmass21"/> Some authors have said the existence of the KBC void violates the assumption that the CMB reflects baryonic density fluctuations at <math>z = 1100</math> or Einstein's theory of [[general relativity]], either of which would violate the ΛCDM model,<ref name="Haslbauer">{{Cite journal|last1=Haslbauer|first1=M|last2=Banik|first2=I|last3=Kroupa|first3=P|date=2020-12-21|title=The KBC void and Hubble tension contradict LCDM on a Gpc scale – Milgromian dynamics as a possible solution|journal=Monthly Notices of the Royal Astronomical Society|volume=499|issue=2|pages=2845–2883|doi=10.1093/mnras/staa2348|arxiv=2009.11292|bibcode=2020MNRAS.499.2845H|issn=0035-8711|doi-access=free}}</ref> while other authors have claimed that supervoids as large as the KBC void are consistent with the ΛCDM model.<ref>{{Cite journal|last1=Sahlén|first1=Martin|last2=Zubeldía|first2=Íñigo|last3=Silk|first3=Joseph|date=2016|title=Cluster–Void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void|journal=The Astrophysical Journal Letters|volume=820|issue=1|pages=L7|doi=10.3847/2041-8205/820/1/L7|issn=2041-8205|arxiv=1511.04075|bibcode=2016ApJ...820L...7S|s2cid=119286482 |doi-access=free }}</ref>

=== Hubble tension ===
{{main|Hubble tension}}
Statistically significant differences remain in values of the Hubble constant derived by matching the ΛCDM model to data from the "early universe", like the cosmic background radiation, compared to values derived from stellar distance measurements, called the "late universe". While systematic error in the measurements remains a possibility, many different kinds of observations agree with one of these two values of the constant. This difference, called the [[Hubble tension]],<ref name="di Valentino 2021 153001">{{cite journal |last1=di Valentino |first1=Eleonora |last2=Mena |first2=Olga |last3=Pan |first3=Supriya |last4=Visnelli |first4=Luca |last5=Yang |first5=Weiqiang |last6=Melchiorri |first6=Alessandro|last7=Mota|first7=David F.|last8=Reiss|first8=Adam G. |last9=Silk|first9=Joseph|author-link9=Joseph Silk|display-authors=3 |date=2021 |title=In the realm of the Hubble tension—a review of solutions |journal=Classical and Quantum Gravity |volume=38 |issue=15 |page=153001 |doi=10.1088/1361-6382/ac086d |arxiv=2103.01183|bibcode=2021CQGra..38o3001D |s2cid=232092525 }}</ref> widely acknowledged to be a major problem for the ΛCDM model.<ref name="cern-courier"/><ref name="LS-20190826">
{{cite news
 |last=Mann |first=Adam
 |title=One Number Shows Something Is Fundamentally Wrong with Our Conception of the Universe – This fight has universal implications
 |url=https://www.livescience.com/hubble-constant-discrepancy-explained.html
 |date=26 August 2019 |work=[[Live Science]] |access-date=26 August 2019
}}</ref><ref name="Snowmass21"/><ref name="Turner"/>

Dozens of proposals for modifications of ΛCDM or completely new models have been published to explain the Hubble tension. Among these models are many that modify the properties of [[dark energy]] or of [[dark matter]] over time, interactions between dark energy and dark matter, unified dark energy and matter, other forms of dark radiation like [[sterile neutrinos]], modifications to the properties of gravity, or the modification of the effects of [[inflation (cosmology)|inflation]], changes to the properties of elementary particles in the early universe, among others. None of these models can simultaneously explain the breadth of other cosmological data as well as ΛCDM.<ref name="di Valentino 2021 153001"/>

=== ''S''<sub>8</sub> tension ===
The "<math>S_8</math> tension" is a name for another question mark for the ΛCDM model.<ref name="Snowmass21"/> The <math>S_8</math> parameter in the ΛCDM model quantifies the amplitude of matter fluctuations in the late universe and is defined as
<math display="block">S_8 \equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}</math>

Early- (e.g. from [[Cosmic microwave background|CMB]] data collected using the Planck observatory) and late-time (e.g. measuring [[weak gravitational lensing]] events) facilitate increasingly precise values of <math>S_8</math>. However, these two categories of measurement differ by more standard deviations than their uncertainties. This discrepancy is called the <math>S_8</math> tension. The name "tension" reflects that the disagreement is not merely between two data sets: the many sets of early- and late-time measurements agree well within their own categories, but there is an unexplained difference between values obtained from different points in the evolution of the universe. Such a tension indicates that the ΛCDM model may be incomplete or in need of correction.<ref name="Snowmass21"/>

Some values for <math>S_8</math> are {{val|0.832|0.013}} (2020 [[Planck (spacecraft)|Planck]]),<ref>{{cite journal |last1=Planck Collaboration |last2=Aghanim |first2=N. |last3=Akrami |first3=Y. |last4=Ashdown |first4=M. |last5=Aumont |first5=J. |last6=Baccigalupi |first6=C. |last7=Ballardini |first7=M. |last8=Banday |first8=A. J. |last9=Barreiro |first9=R. B. |last10=Bartolo |first10=N. |last11=Basak |first11=S. |last12=Battye |first12=R. |last13=Benabed |first13=K. |last14=Bernard |first14=J.-P. |last15=Bersanelli |first15=M. |date=September 2020 |title=Planck 2018 results: VI. Cosmological parameters (Corrigendum) |url=https://www.aanda.org/10.1051/0004-6361/201833910e |journal=Astronomy & Astrophysics |volume=652 |pages=C4 |doi=10.1051/0004-6361/201833910e |issn=0004-6361|hdl=10902/24951 |hdl-access=free }}</ref> {{val|0.766|0.020|0.014}} (2021 [https://kids.strw.leidenuniv.nl/ KIDS]),<ref>{{Cite journal |last1=Heymans |first1=Catherine |last2=Tröster |first2=Tilman |last3=Asgari |first3=Marika |last4=Blake |first4=Chris |last5=Hildebrandt |first5=Hendrik |last6=Joachimi |first6=Benjamin |last7=Kuijken |first7=Konrad |last8=Lin |first8=Chieh-An |last9=Sánchez |first9=Ariel G. |last10=van den Busch |first10=Jan Luca |last11=Wright |first11=Angus H. |last12=Amon |first12=Alexandra |last13=Bilicki |first13=Maciej |last14=de Jong |first14=Jelte |last15=Crocce |first15=Martin |date=February 2021 |title=KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints |url=https://www.aanda.org/10.1051/0004-6361/202039063 |journal=Astronomy & Astrophysics |volume=646 |pages=A140 |doi=10.1051/0004-6361/202039063 |issn=0004-6361|arxiv=2007.15632 |bibcode=2021A&A...646A.140H }}</ref><ref>{{Cite web |last=Wood |first=Charlie |date=8 September 2020 |title=A New Cosmic Tension: The Universe Might Be Too Thin |url=https://www.quantamagazine.org/a-new-cosmic-tension-the-universe-might-be-too-thin-20200908/ |website=[[Quanta Magazine]]}}</ref> {{val|0.776|0.017}} (2022 [[Dark Energy Survey|DES]]),<ref>{{Cite journal |last1=Abbott |first1=T. M. C. |last2=Aguena |first2=M. |last3=Alarcon |first3=A. |last4=Allam |first4=S. |last5=Alves |first5=O. |last6=Amon |first6=A. |last7=Andrade-Oliveira |first7=F. |last8=Annis |first8=J. |last9=Avila |first9=S. |last10=Bacon |first10=D. |last11=Baxter |first11=E. |last12=Bechtol |first12=K. |last13=Becker |first13=M. R. |last14=Bernstein |first14=G. M. |last15=Bhargava |first15=S. |date=2022-01-13 |title=Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and weak lensing |url=https://link.aps.org/doi/10.1103/PhysRevD.105.023520 |journal=Physical Review D |language=en |volume=105 |issue=2 |page=023520 |doi=10.1103/PhysRevD.105.023520 |issn=2470-0010|arxiv=2105.13549 |bibcode=2022PhRvD.105b3520A |hdl=11368/3013060 }}</ref> {{val|0.790|0.018|0.014}} (2023 DES+KIDS),<ref>{{Cite journal |last1=Dark Energy Survey |last2=Kilo-Degree Survey Collaboration |last3=Abbott |first3=T.M.C. |last4=Aguena |first4=M. |last5=Alarcon |first5=A. |last6=Alves |first6=O. |last7=Amon |first7=A. |last8=Andrade-Oliveira |first8=F. |last9=Asgari |first9=M. |last10=Avila |first10=S. |last11=Bacon |first11=D. |last12=Bechtol |first12=K. |last13=Becker |first13=M. R. |last14=Bernstein |first14=G. M. |last15=Bertin |first15=E. |date=2023-10-20 |title=DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys |url=https://astro.theoj.org/article/89164-des-y3-kids-1000-consistent-cosmology-combining-cosmic-shear-surveys |journal=The Open Journal of Astrophysics |volume=6 |page=36 |doi=10.21105/astro.2305.17173 |issn=2565-6120|arxiv=2305.17173 |bibcode=2023OJAp....6E..36D }}</ref> {{val|0.769|0.031|0.034}} – {{val|0.776|0.032|0.033}}<ref>{{Cite journal |last1=Li |first1=Xiangchong |last2=Zhang |first2=Tianqing |last3=Sugiyama |first3=Sunao |last4=Dalal |first4=Roohi |last5=Terasawa |first5=Ryo |last6=Rau |first6=Markus M. |last7=Mandelbaum |first7=Rachel |last8=Takada |first8=Masahiro |last9=More |first9=Surhud |last10=Strauss |first10=Michael A. |last11=Miyatake |first11=Hironao |last12=Shirasaki |first12=Masato |last13=Hamana |first13=Takashi |last14=Oguri |first14=Masamune |last15=Luo |first15=Wentao |date=2023-12-11 |title=Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear two-point correlation functions |url=https://link.aps.org/doi/10.1103/PhysRevD.108.123518 |journal=Physical Review D |language=en |volume=108 |issue=12 |page=123518 |doi=10.1103/PhysRevD.108.123518 |issn=2470-0010|arxiv=2304.00702 |bibcode=2023PhRvD.108l3518L }}</ref><ref>{{Cite journal |last1=Dalal |first1=Roohi |last2=Li |first2=Xiangchong |last3=Nicola |first3=Andrina |last4=Zuntz |first4=Joe |last5=Strauss |first5=Michael A. |last6=Sugiyama |first6=Sunao |last7=Zhang |first7=Tianqing |last8=Rau |first8=Markus M. |last9=Mandelbaum |first9=Rachel |last10=Takada |first10=Masahiro |last11=More |first11=Surhud |last12=Miyatake |first12=Hironao |last13=Kannawadi |first13=Arun |last14=Shirasaki |first14=Masato |last15=Taniguchi |first15=Takanori |date=2023-12-11 |title=Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear power spectra |url=https://link.aps.org/doi/10.1103/PhysRevD.108.123519 |journal=Physical Review D |language=en |volume=108 |issue=12 |page=123519 |doi=10.1103/PhysRevD.108.123519 |issn=2470-0010|arxiv=2304.00701 |bibcode=2023PhRvD.108l3519D }}</ref><ref>{{Cite journal |last=Yoon |first=Mijin |date=2023-12-11 |title=Inconsistency Turns Up Again for Cosmological Observations |url=https://physics.aps.org/articles/v16/193 |journal=Physics |language=en |volume=16 |issue=12 |pages=193 |doi=10.1103/PhysRevD.108.123519|arxiv=2304.00701 |bibcode=2023PhRvD.108l3519D }}</ref><ref>{{Cite web |last=Kruesi |first=Liz |date=19 January 2024 |title=Clashing Cosmic Numbers Challenge Our Best Theory of the Universe |url=https://www.quantamagazine.org/clashing-cosmic-numbers-challenge-our-best-theory-of-the-universe-20240119 |website=[[Quanta Magazine]]}}</ref> (2023 [https://hsc.mtk.nao.ac.jp/ssp/ HSC-SSP]), {{val|0.86|0.01}} (2024 [[EROSITA]]).<ref>{{Cite journal |last1=Ghirardini |first1=V. |last2=Bulbul |first2=E. |last3=Artis |first3=E. |last4=Clerc |first4=N. |last5=Garrel |first5=C. |last6=Grandis |first6=S. |last7=Kluge |first7=M. |last8=Liu |first8=A. |last9=Bahar |first9=Y. E. |last10=Balzer |first10=F. |last11=Chiu |first11=I. |last12=Comparat |first12=J. |last13=Gruen |first13=D. |last14=Kleinebreil |first14=F. |last15=Krippendorf |first15=S. |date=February 2024 |title=The SRG/EROSITA all-sky survey |journal=Astronomy & Astrophysics |volume=689 |pages=A298 |doi=10.1051/0004-6361/202348852 |arxiv=2402.08458}}</ref><ref>{{Cite web |last=Kruesi |first=Liz |date=4 March 2024 |title=Fresh X-Rays Reveal a Universe as Clumpy as Cosmology Predicts |url=https://www.quantamagazine.org/fresh-x-rays-reveal-a-universe-as-clumpy-as-cosmology-predicts-20240304/ |website=[[Quanta Magazine]]}}</ref> Values have also obtained using [[Peculiar velocity|peculiar velocities]], {{val|0.637|0.054}} (2020)<ref>{{Cite journal |last1=Said |first1=Khaled |last2=Colless |first2=Matthew |last3=Magoulas |first3=Christina |last4=Lucey |first4=John R |last5=Hudson |first5=Michael J |date=2020-09-01 |title=Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity |url=https://academic.oup.com/mnras/article/497/1/1275/5870121 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=497 |issue=1 |pages=1275–1293 |doi=10.1093/mnras/staa2032 |doi-access=free |issn=0035-8711|arxiv=2007.04993 }}</ref> and {{val|0.776|0.033}} (2020),<ref>{{Cite journal |last1=Boruah |first1=Supranta S |last2=Hudson |first2=Michael J |last3=Lavaux |first3=Guilhem |date=2020-09-21 |title=Cosmic flows in the nearby Universe: new peculiar velocities from SNe and cosmological constraints |url=https://academic.oup.com/mnras/article/498/2/2703/5894929 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=498 |issue=2 |pages=2703–2718 |doi=10.1093/mnras/staa2485 |doi-access=free |issn=0035-8711|arxiv=1912.09383 }}</ref> among other methods.

=== Axis of evil ===
{{main|Axis of evil (cosmology)}}
{{#section:Axis of evil (cosmology)|lead}}

=== Cosmological lithium problem ===
{{main|Cosmological lithium problem}}

The actual observable amount of lithium in the universe is less than the calculated amount from the ΛCDM model by a factor of 3–4.<ref name=fields11>{{cite journal |last=Fields |first=B. D. |date=2011 |title=The primordial lithium problem |journal=[[Annual Review of Nuclear and Particle Science]] |volume=61 |issue=1 |pages=47–68 |doi=10.1146/annurev-nucl-102010-130445| doi-access=free |arxiv=1203.3551 |bibcode=2011ARNPS..61...47F}}</ref><ref name="Snowmass21"/>{{rp|141}} If every calculation is correct, then solutions beyond the existing ΛCDM model might be needed.<ref name="fields11" />

=== Shape of the universe ===
{{main|Shape of the universe}}
The ΛCDM model assumes that the [[shape of the universe]] is of zero curvature (is flat) and has an undetermined topology. In 2019, interpretation of Planck data suggested that the curvature of the universe might be positive (often called "closed"), which would contradict the ΛCDM model.<ref>{{cite journal|url=https://www.nature.com/articles/s41550-019-0906-9|title=Planck evidence for a closed Universe and a possible crisis for cosmology|author1=Eleonora Di Valentino|author2=Alessandro Melchiorri|author3=Joseph Silk|journal=Nature Astronomy|volume=4|doi=10.1038/s41550-019-0906-9|arxiv=1911.02087|date=4 November 2019|issue=2|pages=196–203|s2cid=207880880|access-date=24 March 2022}}</ref><ref name="Snowmass21"/> Some authors have suggested that the Planck data detecting a positive curvature could be evidence of a local inhomogeneity in the curvature of the universe rather than the universe actually being globally a 3-[[manifold]] of positive curvature.<ref>{{cite journal|url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.87.081301|title=What if Planck's Universe isn't flat?|author1=Philip Bull|author2=Marc Kamionkowski|journal=Physical Review D|volume=87|issue=3|date=15 April 2013|page=081301|doi=10.1103/PhysRevD.87.081301|arxiv=1302.1617|bibcode=2013PhRvD..87h1301B|s2cid=118437535|access-date=24 March 2022}}</ref><ref name="Snowmass21"/>

=== Violations of the strong equivalence principle ===
{{main|Strong equivalence principle}}
The ΛCDM model assumes that the [[strong equivalence principle]] is true. However, in 2020 a group of astronomers analyzed data from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample, together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. They concluded that there was highly statistically significant evidence of violations of the strong equivalence principle in weak gravitational fields in the vicinity of rotationally supported galaxies.<ref>{{Cite journal|arxiv = 2009.11525|doi = 10.3847/1538-4357/abbb96|title = Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies|year = 2020|last1 = Chae|first1 = Kyu-Hyun|last2 = Lelli|first2 = Federico|last3 = Desmond|first3 = Harry|last4 = McGaugh|first4 = Stacy S.|last5 = Li|first5 = Pengfei|last6 = Schombert|first6 = James M.|journal = The Astrophysical Journal|volume = 904|issue = 1|page = 51|bibcode = 2020ApJ...904...51C|s2cid = 221879077 | doi-access=free }}</ref> They observed an effect inconsistent with [[tidal force|tidal effects]] in the ΛCDM model. These results have been challenged as failing to consider inaccuracies in the rotation curves and correlations between galaxy properties and clustering strength.<ref>{{Cite journal |last1=Paranjape |first1=Aseem |last2=Sheth |first2=Ravi K |date=2022-10-04 |title=The phenomenology of the external field effect in cold dark matter models |url=https://academic.oup.com/mnras/article/517/1/130/6713954 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=517 |issue=1 |pages=130–139 |doi=10.1093/mnras/stac2689 |doi-access=free |issn=0035-8711|arxiv=2112.00026 }}</ref> and as inconsistent with similar analysis of other galaxies.<ref>{{Cite journal |last1=Freundlich |first1=Jonathan |last2=Famaey |first2=Benoit |last3=Oria |first3=Pierre-Antoine |last4=Bílek |first4=Michal |last5=Müller |first5=Oliver |last6=Ibata |first6=Rodrigo |date=2022-02-01 |title=Probing the radial acceleration relation and the strong equivalence principle with the Coma cluster ultra-diffuse galaxies |url=https://www.aanda.org/articles/aa/abs/2022/02/aa42060-21/aa42060-21.html |journal=Astronomy & Astrophysics |language=en |volume=658 |pages=A26 |doi=10.1051/0004-6361/202142060 |issn=0004-6361 |quote=We hence do not see any evidence for a violation of the strong equivalence principle in Coma cluster UDGs, contrarily to, for instance, Chae et al. (2020, 2021), for disc galaxies in the field. Our work extends that of Bílek et al. (2019b) and Haghi et al. (2019a), which is limited to DF44 and makes the result all the more compelling. We recall that the MOND predictions do not involve any free parameter.

|doi-access=free |arxiv=2109.04487 |bibcode=2022A&A...658A..26F }}</ref>

=== Cold dark matter discrepancies ===
{{main|Cold dark matter#Challenges}}
Several discrepancies between the predictions of [[cold dark matter]] in the ΛCDM model and observations of galaxies and their clustering have arisen. Some of these problems have proposed solutions, but it remains unclear whether they can be solved without abandoning the ΛCDM model.<ref>{{Cite journal |arxiv=1006.1647 |title=Local-Group tests of dark-matter Concordance Cosmology: Towards a new paradigm for structure formation |year=2010 |last1=Kroupa |first1=P. |last2=Famaey |first2=B. |last3=de Boer |first3=Klaas S. |last4=Dabringhausen |first4=Joerg |last5=Pawlowski |first5=Marcel |last6=Boily |first6=Christian |last7=Jerjen |first7=Helmut |last8=Forbes |first8=Duncan |last9=Hensler |first9=Gerhard |journal=Astronomy and Astrophysics |volume=523 |pages=32–54 |doi=10.1051/0004-6361/201014892 |bibcode=2010A&A...523A..32K|s2cid=11711780 }}</ref>

[[Mordehai Milgrom|Milgrom]], [[Stacy McGaugh|McGaugh]], and [[Pavel Kroupa|Kroupa]] have criticized the dark matter portions of the theory from the perspective of [[galaxy formation]] models and supporting the alternative [[modified Newtonian dynamics]] (MOND) theory, which requires a modification of the [[Einstein field equations]] and the [[Friedmann equations]] as seen in proposals such as [[modified gravity theory]] (MOG theory) or [[tensor–vector–scalar gravity]] theory (TeVeS theory).{{citation needed|date=January 2025}} Other proposals by theoretical astrophysicists of cosmological alternatives to Einstein's general relativity that attempt to account for dark energy or dark matter include [[f(R) gravity]], [[Scalar–tensor theory|scalar–tensor theories]] such as {{ill|galileon|ko}} theories (see [[Galilean invariance]]), [[brane cosmology|brane cosmologies]], the [[DGP model]], and [[massive gravity]] and its extensions such as [[bimetric theory|bimetric gravity]].{{citation needed|date=February 2024}}

==== Cuspy halo problem ====
{{main|Cuspy halo problem}}
The density distributions of dark matter halos in cold dark matter simulations (at least those that do not include the impact of baryonic feedback) are much more peaked than what is observed in galaxies by investigating their rotation curves.<ref>{{Cite journal |title=The cored distribution of dark matter in spiral galaxies|year=2004 |last1=Gentile |first1=G. |last2=Salucci |first2=P. |journal=Monthly Notices of the Royal Astronomical Society |volume=351 |issue=3 |pages=903–922 |doi=10.1111/j.1365-2966.2004.07836.x |doi-access=free |arxiv=astro-ph/0403154 |bibcode = 2004MNRAS.351..903G|s2cid=14308775 }}</ref>

==== Dwarf galaxy problem ====
{{main|Dwarf galaxy problem}} 
Cold dark matter simulations predict large numbers of small dark matter halos, more numerous than the number of small dwarf galaxies that are observed around galaxies like the [[Milky Way]].<ref name=Klypin>{{cite journal |last1=Klypin |first1=Anatoly |last2=Kravtsov |first2=Andrey V. |last3=Valenzuela |first3=Octavio |last4=Prada |first4=Francisco |year=1999 |title=Where are the missing galactic satellites? |journal=Astrophysical Journal |volume=522 |issue=1 |pages=82–92 |doi=10.1086/307643 |bibcode=1999ApJ...522...82K |arxiv=astro-ph/9901240|s2cid=12983798 }}</ref>

==== Satellite disk problem ====
Dwarf galaxies around the [[Milky Way]] and [[Andromeda Galaxy|Andromeda]] galaxies are observed to be orbiting in thin, planar structures whereas the simulations predict that they should be distributed randomly about their parent galaxies.<ref name=Pawlowski>{{cite journal |first1=Marcel |last1=Pawlowski |display-authors=etal |title=Co-orbiting satellite galaxy structures are still in conflict with the distribution of primordial dwarf galaxies |journal=Monthly Notices of the Royal Astronomical Society |volume=442 |issue=3 |pages=2362–2380 |year=2014 |arxiv=1406.1799|doi=10.1093/mnras/stu1005 |doi-access=free |bibcode=2014MNRAS.442.2362P }}</ref> However, latest research suggests this seemingly bizarre alignment is just a quirk which will dissolve over time.<ref name="Sawala">{{cite journal |first1=Till |last1=Sawala |first2=Marius |last2=Cautun |first3=Carlos |last3=Frenk |display-authors=etal |title=The Milky Way's plane of satellites: consistent with ΛCDM|journal=Nature Astronomy |year=2022 |volume=7 |issue=4 |pages=481–491 |arxiv=2205.02860|doi=10.1038/s41550-022-01856-z |bibcode=2023NatAs...7..481S|s2cid=254920916 }}</ref>

==== High-velocity galaxy problem ====
Galaxies in the [[NGC 3109]] association are moving away too rapidly to be consistent with expectations in the ΛCDM model.<ref>{{Cite journal|last1=Banik|first1=Indranil|last2=Zhao|first2=H|date=2018-01-21|title=A plane of high velocity galaxies across the Local Group|journal=Monthly Notices of the Royal Astronomical Society|volume=473|issue=3|pages=4033–4054|doi=10.1093/mnras/stx2596|arxiv=1701.06559|bibcode=2018MNRAS.473.4033B|issn=0035-8711|doi-access=free}}</ref> In this framework, [[NGC 3109]] is too massive and distant from the [[Local Group]] for it to have been flung out in a three-body interaction involving the [[Milky Way]] or [[Andromeda Galaxy]].<ref>{{Cite journal|last1=Banik|first1=Indranil|last2=Haslbauer|first2=Moritz|last3=Pawlowski|first3=Marcel S.|last4=Famaey|first4=Benoit|last5=Kroupa|first5=Pavel|date=2021-06-21|title=On the absence of backsplash analogues to NGC 3109 in the ΛCDM framework|journal=Monthly Notices of the Royal Astronomical Society|volume=503|issue=4|pages=6170–6186|doi=10.1093/mnras/stab751|arxiv=2105.04575|bibcode=2021MNRAS.503.6170B|issn=0035-8711|doi-access=free}}</ref>

==== Galaxy morphology problem ====
If galaxies grew hierarchically, then massive galaxies required many mergers. [[Galaxy merger|Major mergers]] inevitably create a classical [[Bulge (astronomy)|bulge]]. On the contrary, about 80% of observed galaxies give evidence of no such bulges, and giant pure-disc galaxies are commonplace.<ref name="kormendy2010">{{cite journal |last1=Kormendy |first1=J. |author1-link=John Kormendy |last2=Drory |first2=N. |last3=Bender |first3=R. |last4=Cornell |first4=M.E. |title=Bulgeless giant galaxies challenge our picture of galaxy formation by hierarchical clustering |year=2010 |journal=[[The Astrophysical Journal]] |volume=723 |issue=1 |pages=54–80 |doi=10.1088/0004-637X/723/1/54 |arxiv=1009.3015 |bibcode=2010ApJ...723...54K|s2cid=119303368 }}</ref> The tension can be quantified by comparing the observed distribution of galaxy shapes today with predictions from high-resolution hydrodynamical cosmological simulations in the ΛCDM framework, revealing a highly significant problem that is unlikely to be solved by improving the resolution of the simulations.<ref name="Haslbauer2022">{{cite journal |last1=Haslbauer|first1=M|last2=Banik|first2=I|last3=Kroupa|first3=P|last4=Wittenburg|first4=N|last5=Javanmardi|first5=B|title=The High Fraction of Thin Disk Galaxies Continues to Challenge ΛCDM Cosmology|date=2022-02-01|journal=[[The Astrophysical Journal]]|volume=925|issue=2|page=183|doi=10.3847/1538-4357/ac46ac|issn=1538-4357|arxiv=2202.01221|bibcode=2022ApJ...925..183H|doi-access=free}}</ref> The high bulgeless fraction was nearly constant for 8&nbsp;billion years.<ref name="sachdeva2016">{{cite journal |last1=Sachdeva |first1=S. |last2=Saha |first2=K. |title=Survival of pure disk galaxies over the last 8&nbsp;billion years |year=2016 |journal=The Astrophysical Journal Letters |volume=820 |issue=1 |pages=L4 |doi=10.3847/2041-8205/820/1/L4 |arxiv=1602.08942 |bibcode=2016ApJ...820L...4S|s2cid=14644377 |doi-access=free }}</ref>

==== Fast galaxy bar problem ====
If galaxies were embedded within massive halos of [[cold dark matter]], then the bars that often develop in their central regions would be slowed down by [[dynamical friction]] with the halo. This is in serious tension with the fact that observed galaxy bars are typically fast.<ref name="Roshan2021">{{Cite journal|last1=Mahmood|first1=R|last2=Ghafourian|first2=N|last3=Kashfi|first3=T|last4=Banik|first4=I|last5=Haslbauer|first5=M|last6=Cuomo|first6=V|last7=Famaey|first7=B|last8=Kroupa|first8=P|date=2021-11-01|title=Fast galaxy bars continue to challenge standard cosmology|journal=Monthly Notices of the Royal Astronomical Society|volume=508|issue=1|pages=926–939|doi=10.1093/mnras/stab2553|doi-access=free|arxiv=2106.10304|bibcode=2021MNRAS.508..926R|hdl=10023/24680|issn=0035-8711}}</ref>

==== Small scale crisis ====
Comparison of the model with observations may have some problems on sub-galaxy scales, possibly predicting [[Dwarf galaxy problem|too many dwarf galaxies]] and too much dark matter in the innermost regions of galaxies. This problem is called the "small scale crisis".<ref>{{Cite journal
 | title =Synopsis: Tackling the Small-Scale Crisis
 |journal = Physical Review D|volume = 95|issue = 12|page = 121302| last =Rini
 | first =Matteo
 |doi = 10.1103/PhysRevD.95.121302|year = 2017|arxiv = 1703.10559|bibcode = 2017PhRvD..95l1302N|s2cid = 54675159}}</ref>  These small scales are harder to resolve in computer simulations, so it is not yet clear whether the problem is the simulations, non-standard properties of dark matter, or a more radical error in the model.

==== High redshift galaxies ====
Observations from the [[James Webb Space Telescope]] have resulted in various galaxies confirmed by [[spectroscopy]] at high redshift, such as [[JADES-GS-z13-0]] at [[cosmological redshift]] of 13.2.<ref name="NASA-milestone">{{cite web|title = NASA's Webb Reaches New Milestone in Quest for Distant Galaxies|url = https://blogs.nasa.gov/webb/2022/12/09/nasas-webb-reaches-new-milestone-in-quest-for-distant-galaxies/|first = Thaddeus|last = Cesari|date = 9 December 2022|access-date = 9 December 2022}}</ref><ref name="Curtis-Lake2022">{{cite web|display-authors = etal|first1 = Emma|last1 = Curtis-Lake|title = Spectroscopy of four metal-poor galaxies beyond redshift ten|url = https://webbtelescope.org/files/live/sites/webb/files/home/webb-science/early-highlights/_documents/2022-061-jades/JADES_CurtisLake.pdf|date = December 2022| arxiv=2212.04568 }}</ref> Other candidate galaxies which have not been confirmed by spectroscopy include [[CEERS-93316]] at cosmological [[redshift]] of 16.4.

Existence of surprisingly massive galaxies in the early universe challenges the preferred models describing how dark matter halos drive galaxy formation. It remains to be seen whether a revision of the Lambda-CDM model with parameters given by Planck Collaboration is necessary to resolve this issue. The discrepancies could also be explained by particular properties (stellar masses or effective volume) of the candidate galaxies, yet unknown force or particle outside of the [[Standard Model]] through which dark matter interacts, more efficient baryonic matter accumulation by the dark matter halos, early dark energy models,<ref name="SmithEtAl-2022">{{cite journal|title=Hints of early dark energy in Planck, SPT, and ACT data: New physics or systematics?|author1=Smith, Tristian L.|author2=Lucca, Matteo|author3=Poulin, Vivian|author4=Abellan, Guillermo F.|author5=Balkenhol, Lennart|author6=Benabed, Karim|author7=Galli, Silvia|author8=Murgia, Riccardo|journal=Physical Review D|volume=106|issue=4|date=August 2022|page=043526 |doi=10.1103/PhysRevD.106.043526|arxiv=2202.09379|bibcode=2022PhRvD.106d3526S|s2cid=247011465 }}</ref> or the hypothesized long-sought [[Population III stars]].<ref name="Boylan-Kolchin">{{cite journal|title=Stress testing ΛCDM with high-redshift galaxy candidates|first=Michael|last=Boylan-Kolchin|journal=Nature Astronomy |year=2023 |volume=7 |issue=6 |pages=731–735 |doi=10.1038/s41550-023-01937-7 |pmid=37351007 |pmc=10281863 |arxiv=2208.01611|bibcode=2023NatAs...7..731B |s2cid=251252960 }}</ref><ref name="SciAm2022">{{cite web|title=Astronomers Grapple with JWST's Discovery of Early Galaxies|url=https://www.scientificamerican.com/article/astronomers-grapple-with-jwsts-discovery-of-early-galaxies1/|last=O'Callaghan|first=Jonathan|website=[[Scientific American]] |date=6 December 2022|access-date=10 December 2022}}</ref><ref name="BehrooziEtAl">{{cite journal|title=The Universe at z > 10: predictions for JWST from the UNIVERSEMACHINE DR1|author1= Behroozi, Peter|author2=Conroy, Charlie|author3=Wechsler, Risa H.|author4=Hearin, Andrew|author5=Williams, Christina C.|author6=Moster, Benjamin P.|author7=Yung, L. Y. Aaron|author8=Somerville, Rachel S.|author9=Gottlöber, Stefan|author10=Yepes, Gustavo|author11=Endsley, Ryan|journal=Monthly Notices of the Royal Astronomical Society|volume=499|issue=4|pages=5702–5718|date=December 2020|doi=10.1093/mnras/staa3164|doi-access= free|arxiv=2007.04988|bibcode=2020MNRAS.499.5702B}}</ref><ref name="SpringelHernquist">{{cite journal|title=The history of star formation in a Λ cold dark matter universe|author1=Volker Springel|author2=Lars Hernquist|journal=Monthly Notices of the Royal Astronomical Society|volume=339|issue=2|pages=312–334|date=February 2003|doi=10.1046/j.1365-8711.2003.06207.x|doi-access=free |arxiv=astro-ph/0206395|bibcode=2003MNRAS.339..312S |s2cid=8715136 }}</ref>

=== Missing baryon problem ===
{{main|Missing baryon problem}}
Massimo Persic and Paolo Salucci<ref>{{Cite journal|last1=Persic|first1=M.|last2=Salucci|first2=P.|date=1992-09-01|title=The baryon content of the Universe|journal=Monthly Notices of the Royal Astronomical Society|volume=258|issue=1|pages=14P–18P|doi=10.1093/mnras/258.1.14P|arxiv=astro-ph/0502178|bibcode=1992MNRAS.258P..14P |issn=0035-8711|doi-access=free}}</ref> first estimated the baryonic density today present in ellipticals, spirals, groups and clusters of galaxies.
They performed an integration of the baryonic mass-to-light ratio over luminosity (in the following <math display="inline">  M_{\rm b}/L </math>), weighted with the luminosity function <math display="inline">\phi(L)</math> over the previously mentioned classes of astrophysical objects:

<math display="block">\rho_{\rm b} = \sum \int L\phi(L) \frac{M_{\rm b}}{L} \, dL.</math>

The result was:

<math display="block"> \Omega_{\rm b}=\Omega_*+\Omega_\text{gas}=2.2\times10^{-3}+1.5\times10^{-3}\;h^{-1.3}\simeq0.003 ,</math>

where <math> h\simeq 0.72 </math>.

Note that this value is much lower than the prediction of standard cosmic nucleosynthesis <math> \Omega_{\rm b}\simeq0.0486 </math>, so that stars and gas in galaxies and in galaxy groups and clusters account for less than 10% of the primordially synthesized baryons. This issue is known as the problem of the "missing baryons".

The missing baryon problem is claimed to be resolved. Using observations of the kinematic [[Sunyaev–Zeldovich effect|Sunyaev–Zel'dovich effect]] spanning more than 90% of the lifetime of the Universe, in 2021 astrophysicists found that approximately 50% of all baryonic matter is outside [[dark matter halo]]es, filling the space between galaxies.<ref>{{Cite journal|last1=Chaves-Montero|first1=Jonás|last2=Hernández-Monteagudo|first2=Carlos|last3=Angulo|first3=Raúl E|last4=Emberson|first4=J D|date=2021-03-25|title=Measuring the evolution of intergalactic gas from z = 0 to 5 using the kinematic Sunyaev–Zel'dovich effect|url=https://academic.oup.com/mnras/article/503/2/1798/6184230|journal=Monthly Notices of the Royal Astronomical Society|language=en|volume=503|issue=2|pages=1798–1814|doi=10.1093/mnras/staa3782|doi-access=free |arxiv=1911.10690 |issn=0035-8711}}</ref> Together with the amount of baryons inside galaxies and surrounding them, the total amount of baryons in the late time Universe is compatible with early Universe measurements.

=== Conventionalism ===
It has been argued that the ΛCDM model has adopted [[conventionalism|conventionalist stratagems]], rendering it [[falsifiability|unfalsifiable]] in the sense defined by [[Karl Popper]]. When faced with new data not in accord with a prevailing model, the conventionalist will find ways to adapt the theory rather than declare it false. Thus dark matter was added after the observations of anomalous galaxy rotation rates. [[Thomas Kuhn]] viewed the process differently, as "problem solving" within the existing paradigm.<ref>{{Cite journal | doi=10.1016/j.shpsb.2016.12.002| title=Cosmology and convention| journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics| volume=57| pages=41–52| year=2017| last1=Merritt| first1=David| arxiv=1703.02389| bibcode=2017SHPMP..57...41M| s2cid=119401938}}</ref>