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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 |last1=Fu |first1=L. |last2=Kilbinger |first2=M. |last3=Erben |first3=T. |last4=Heymans |first4=C. |last5=Hildebrandt |first5=H. |last6=Hoekstra |first6=H. |last7=Kitching |first7=T. D. |last8=Mellier |first8=Y. |last9=Miller |first9=L. |last10=Semboloni |first10=E. |last11=Simon |first11=P. |last12=Van Waerbeke |first12=L. |last13=Coupon |first13=J. |last14=Harnois-Deraps |first14=J. |last15=Hudson |first15=M. J. |date=2014-05-26 |title=CFHTLenS: cosmological constraints from a combination of cosmic shear two-point and three-point correlations |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=441 |issue=3 |pages=2725–2743 |doi=10.1093/mnras/stu754 |doi-access=free |issn=0035-8711}}</ref><ref>{{Cite journal |last1=Abdalla |first1=Elcio |last2=Abellán |first2=Guillermo Franco |last3=Aboubrahim |first3=Amin |last4=Agnello |first4=Adriano |last5=Akarsu |first5=Özgür |last6=Akrami |first6=Yashar |last7=Alestas |first7=George |last8=Aloni |first8=Daniel |last9=Amendola |first9=Luca |last10=Anchordoqui |first10=Luis A. |last11=Anderson |first11=Richard I. |last12=Arendse |first12=Nikki |last13=Asgari |first13=Marika |last14=Ballardini |first14=Mario |last15=Barger |first15=Vernon |date=June 2022 |title=Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies |url=https://linkinghub.elsevier.com/retrieve/pii/S2214404822000179 |journal=Journal of High Energy Astrophysics |language=en |volume=34 |pages=49–211 |doi=10.1016/j.jheap.2022.04.002 |arxiv=2203.06142 |bibcode=2022JHEAp..34...49A }}</ref>. In recent years much larger surveys have been carried out, some of the preliminarily results also showed evidence of the same tension<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 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><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>. However, other projects found that with increasing precision there was no significant tension, finding consistency with the Planck results<ref>{{Citation |last1=Wright |first1=Angus H. |title=KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey |date=2025 |url=https://arxiv.org/abs/2503.19441 |access-date=2025-07-24 |arxiv=2503.19441 |last2=Stölzner |first2=Benjamin |last3=Asgari |first3=Marika |last4=Bilicki |first4=Maciej |last5=Giblin |first5=Benjamin |last6=Heymans |first6=Catherine |last7=Hildebrandt |first7=Hendrik |last8=Hoekstra |first8=Henk |last9=Joachimi |first9=Benjamin}}</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><ref>{{Cite web |title=eROSITA relaxes cosmological tension |url=https://www.mpg.de/21542664/erosita-confirms-standard-model-of-cosmology |access-date=2025-07-24 |website=www.mpg.de |language=en}}</ref>.
=== Axis of evil ===
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==== High redshift galaxies ====
There has been debate on whether early massive galaxies and supermassive black holes are in conflict with LCDM<ref>{{Cite journal |lastlast1=Steinhardt |firstfirst1=Charles. L. |last2=Capak |first2=Peter |last3=Masters |first3=Dan |last4=Speagle |first4=Josh S. |date=2016-06-10 |title=THEThe IMPOSSIBLYImpossibly EARLYEarly GALAXYGalaxy PROBLEM |url=https://iopscience.iop.org/article/10.3847/0004-637X/824/1/21Problem |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 |lastlast1=Behroozi |firstfirst1=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 Web Space Telescope]], a team of astronomers selected candidate massive galaxies in the early universe.<ref>{{Cite journal |lastlast1=Labbé |firstfirst1=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 2023-04 |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 |lastlast1=Kocevski |firstfirst1=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 2025-06 |title=The Rise of Faint, Red Active Galactic Nuclei at z > 4: A Sample of Little Red Dots in the JWST Extragalactic Legacy Fields |url=https://ui.adsabs.harvard.edu/abs/2025ApJ...986..126K/abstract |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 |lastlast1=McCaffrey |firstfirst1=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 |lastlast1=Xiao |firstfirst1=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 2024-11 |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 |lastlast1=Yung |firstfirst1=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 |publisherarxiv=arXiv |doi=10.48550/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 |lastlast1=Sun |firstfirst1=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 |url=https://iopscience.iop.org/article/10.3847/2041-8213/acf85a |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 |lastlast1=Dekel |firstfirst1=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>
