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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|
==== Violations of homogeneity ====
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[[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}}
=== Hubble tension ===
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=== ''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) and late-time (e.g. measuring [[weak gravitational lensing]]) measurements facilitate increasingly precise values of <math>S_8</math>. Results from initial weak lensing measurements found a lower value of <math>S_8</math>, compared to the value estimated from Planck<ref>{{Cite journal |
=== Axis of evil ===
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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>
There has been debate on whether early massive galaxies and supermassive black holes are in conflict with LCDM<ref>{{Cite journal |last1=Steinhardt |first1=Charles. L. |last2=Capak |first2=Peter |last3=Masters |first3=Dan |last4=Speagle |first4=Josh S. |date=2016-06-10 |title=The Impossibly Early Galaxy Problem |journal=The Astrophysical Journal |volume=824 |issue=1 |pages=21 |doi=10.3847/0004-637X/824/1/21 |arxiv=1506.01377 |bibcode=2016ApJ...824...21S |doi-access=free |issn=0004-637X}}</ref>. To make such a comparison, one must model the complex physics of galaxy formation, as well as the underlying LCDM cosmology.<ref>{{Cite journal |last1=Behroozi |first1=Peter |last2=Silk |first2=Joseph |date=2018-07-11 |title=The most massive galaxies and black holes allowed by ΛCDM |url=https://academic.oup.com/mnras/article/477/4/5382/4975781 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=477 |issue=4 |pages=5382–5387 |doi=10.1093/mnras/sty945 |doi-access=free |issn=0035-8711}}</ref> Tests using galaxies are therefore less direct, as they require assumptions about how galaxies form.
Using some of the first data from the [[James Webb Space Telescope]], a team of astronomers selected candidate massive galaxies in the early universe.<ref>{{Cite journal |last1=Labbé |first1=Ivo |last2=van Dokkum |first2=Pieter |last3=Nelson |first3=Erica |last4=Bezanson |first4=Rachel |last5=Suess |first5=Katherine A. |last6=Leja |first6=Joel |last7=Brammer |first7=Gabriel |last8=Whitaker |first8=Katherine |last9=Mathews |first9=Elijah |last10=Stefanon |first10=Mauro |last11=Wang |first11=Bingjie |date=April 2023 |title=A population of red candidate massive galaxies ~600 Myr after the Big Bang |url=https://www.nature.com/articles/s41586-023-05786-2 |journal=Nature |language=en |volume=616 |issue=7956 |pages=266–269 |doi=10.1038/s41586-023-05786-2 |pmid=36812940 |arxiv=2207.12446 |bibcode=2023Natur.616..266L |issn=1476-4687}}</ref> The existence of such massive galaxies in the early universe would challenge standard cosmology. <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> Follow up spectroscopy revealed that most of these objects have [[Active galactic nucleus|Active Galactic Nuclei]], which boosts the galaxies brightness and caused the masses to be overestimated. <ref>{{Cite web |date=2025-07-01 |title=JWST's early galaxies didn't break the Universe. They revealed it. |url=https://bigthink.com/starts-with-a-bang/jwst-break-universe-revealed/ |access-date=2025-07-24 |website=Big Think |language=en-US}}</ref><ref>{{Cite journal |last1=Kocevski |first1=Dale D. |last2=Finkelstein |first2=Steven L. |last3=Barro |first3=Guillermo |last4=Taylor |first4=Anthony J. |last5=Calabrò |first5=Antonello |last6=Laloux |first6=Brivael |last7=Buchner |first7=Johannes |last8=Trump |first8=Jonathan R. |last9=Leung |first9=Gene C. K. |last10=Yang |first10=Guang |last11=Dickinson |first11=Mark |last12=Pérez-González |first12=Pablo G. |last13=Pacucci |first13=Fabio |last14=Inayoshi |first14=Kohei |last15=Somerville |first15=Rachel S. |date=June 2025 |title=The Rise of Faint, Red Active Galactic Nuclei at z > 4: A Sample of Little Red Dots in the JWST Extragalactic Legacy Fields |journal=The Astrophysical Journal |language=en |volume=986 |issue=2 |pages=126 |doi=10.3847/1538-4357/adbc7d |arxiv=2404.03576 |bibcode=2025ApJ...986..126K |doi-access=free |issn=0004-637X}}</ref> The high redshift galaxies which have been spectroscopically confirmed, such as [[JADES-GS-z13-0]], are much less massive and are consistent with the predictions from LCDM simulations run before JWST<ref>{{Cite journal |last1=McCaffrey |first1=Joe |last2=Hardin |first2=Samantha |last3=Wise |first3=John H. |last4=Regan |first4=John A. |date=2023-09-27 |title=No Tension: JWST Galaxies at \(z > 10\) Consistent with Cosmological Simulations |url=http://localhost:58547/article/88302-no-tension-jwst-galaxies-at-z-10-consistent-with-cosmological-simulations,%20https://astro.theoj.org/article/88302-no-tension-jwst-galaxies-at-z-10-consistent-with-cosmological-simulations |journal=The Open Journal of Astrophysics |language=en |volume=6 |page=47 |doi=10.21105/astro.2304.13755 |arxiv=2304.13755 |bibcode=2023OJAp....6E..47M }}</ref>. As a population, the confirmed high redshift galaxies are brighter than expected from simulations, but not to the extent that they violate cosmological limits.<ref>{{Cite journal |last1=Xiao |first1=Mengyuan |last2=Oesch |first2=Pascal A. |last3=Elbaz |first3=David |last4=Bing |first4=Longji |last5=Nelson |first5=Erica J. |last6=Weibel |first6=Andrea |last7=Illingworth |first7=Garth D. |last8=van Dokkum |first8=Pieter |last9=Naidu |first9=Rohan P. |last10=Daddi |first10=Emanuele |last11=Bouwens |first11=Rychard J. |last12=Matthee |first12=Jorryt |last13=Wuyts |first13=Stijn |last14=Chisholm |first14=John |last15=Brammer |first15=Gabriel |date=November 2024 |title=Accelerated formation of ultra-massive galaxies in the first billion years |url=https://ui.adsabs.harvard.edu/abs/2024Natur.635..311X/abstract |journal=Nature |language=en |volume=635 |issue=8038 |pages=311–315 |doi=10.1038/s41586-024-08094-5 |pmid=39537883 |arxiv=2309.02492 |bibcode=2024Natur.635..311X |issn=0028-0836}}</ref><ref>{{Citation |last1=Yung |first1=L. Y. Aaron |title=$Λ$CDM is still not broken: empirical constraints on the star formation efficiency at $z \sim 12-30$ |date=2025 |url=https://arxiv.org/abs/2504.18618 |access-date=2025-07-24 |arxiv=2504.18618 |last2=Somerville |first2=Rachel S. |last3=Iyer |first3=Kartheik G.}}</ref> Theorists are studying many possible explanations, including modifying cosmology, more efficient star formation and different stellar populations.<ref>{{Cite journal |last1=Sun |first1=Guochao |last2=Faucher-Giguère |first2=Claude-André |last3=Hayward |first3=Christopher C. |last4=Shen |first4=Xuejian |last5=Wetzel |first5=Andrew |last6=Cochrane |first6=Rachel K. |date=2023-10-01 |title=Bursty Star Formation Naturally Explains the Abundance of Bright Galaxies at Cosmic Dawn |journal=The Astrophysical Journal Letters |volume=955 |issue=2 |pages=L35 |doi=10.3847/2041-8213/acf85a |arxiv=2307.15305 |bibcode=2023ApJ...955L..35S |doi-access=free |issn=2041-8205}}</ref><ref>{{Cite journal |last1=Dekel |first1=Avishai |last2=Sarkar |first2=Kartick C |last3=Birnboim |first3=Yuval |last4=Mandelker |first4=Nir |last5=Li |first5=Zhaozhou |date=2023-06-08 |title=Efficient formation of massive galaxies at cosmic dawn by feedback-free starbursts |url=https://academic.oup.com/mnras/article/523/3/3201/7179993 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=523 |issue=3 |pages=3201–3218 |doi=10.1093/mnras/stad1557 |doi-access=free |issn=0035-8711}}</ref>
=== Missing baryon problem ===
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Extended models allow one or more of the "fixed" parameters above to vary, in addition to the basic six; so these models join smoothly to the basic six-parameter model in the limit that the additional parameter(s) approach the default values. For example, possible extensions of the simplest ΛCDM model allow for spatial curvature (<math>\Omega_\text{tot}</math> may be different from 1); or [[quintessence (physics)|quintessence]] rather than a [[cosmological constant]] where the [[Equation of state (cosmology)|equation of state]] of dark energy is allowed to differ from −1. Cosmic inflation predicts tensor fluctuations ([[gravitational wave]]s). Their amplitude is parameterized by the tensor-to-scalar ratio (denoted <math>r</math>), which is determined by the unknown energy scale of inflation. Other modifications allow [[hot dark matter]] in the form of [[neutrino]]s more massive than the minimal value, or a running spectral index; the latter is generally not favoured by simple cosmic inflation models.
Allowing additional variable parameter(s) will generally ''increase'' the uncertainties in the standard six parameters quoted above, and may also shift the central values slightly. The table
Some researchers have suggested that there is a running spectral index, but no statistically significant study has revealed one. Theoretical expectations suggest that the tensor-to-scalar ratio <math>r</math> should be between 0 and 0.3, and the latest results are within those limits.
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