Lambda-CDM model: Difference between revisions

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=== ''S''₈ 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 |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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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 redshift galaxies ====

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.

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.

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 &gt; 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>

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 ===

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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&nbsp;−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 belowabove shows results for each of the possible "6+1" scenarios with one additional variable parameter; this indicates that, as of 2015, there is no convincing evidence that any additional parameter is different from its default value.

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.