Editing Lambda-CDM model (section)

=== ''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.