Lambda-CDM model: Difference between revisions

Revision as of 06:34, 2 June 2025

Revision as of 02:23, 19 June 2025

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# A postulate by [[Hermann Weyl]] that the lines of spacetime ([[geodesics]]) intersect at only one point, where time along each line can be synchronized; the behavior resembles an expanding [[perfect fluid]],<ref name="Longair-2009"/>{{rp|175}}

# [[general relativity]] that relates the geometry of spacetime to the distribution of matter and energy.

This combination greatly simplifies the equations of general relativity into a form called the [[Friedmann equations]]. These equations specify the evolution of the [[Scale factor (cosmology)|scale factor]] of the universe in terms of the pressure and density of a perfect fluid. The evolving density is composed of different kinds of energy and matter, each with its own role in affecting the scale factor.<ref>{{Cite book |last=White |first=Simon |title=Physics of the Early Universe: Proceedings of the Thirty Sixth Scottish Universities Summer School in Physics, Edinburgh, July 24 - August 11 1989 |date=1990 |publisher=Taylor & Francis Group |isbn=978-1-040-29413-0 |edition=1 |series=Scottish Graduate Series |___location=Milton |chapter=Physical Cosmology}}</ref>{{rp|7}} For example, a model might include [[baryons]], [[photons]], [[neutrinos]], and [[dark matter]].<ref name=PDG-2024>{{Cite journal |lastlast1=Navas |firstfirst1=S. |last2=Amsler |first2=C. |last3=Gutsche |first3=T. |last4=Hanhart |first4=C. |last5=Hernández-Rey |first5=J. J J. |last6=Lourenço |first6=C. |last7=Masoni |first7=A. |last8=Mikhasenko |first8=M. |last9=Mitchell |first9=R. E E. |last10=Patrignani |first10=C. |last11=Schwanda |first11=C. |last12=Spanier |first12=S. |last13=Venanzoni |first13=G. |last14=Yuan |first14=C. Z Z. |last15=Agashe |first15=K. |date=2024-08-01 |title=Review of Particle Physics |url=https://link.aps.org/doi/10.1103/PhysRevD.110.030001 |journal=Physical Review D |language=en |volume=110 |issue=3 |page=030001 |doi=10.1103/PhysRevD.110.030001 |issn=2470-0010|hdl=11384/149923 |hdl-access=free }}</ref>{{rp|25.1.1}} These component densities become parameters extracted when the model is constrained to match astrophysical observations. The model aims to describe the observable universe from approximately 0.1&nbsp;s to the present.<ref name=DeruelleUzan/>{{rp|605}}

The most accurate observations which are sensitive to the component densities are consequences of statistical inhomogeneity called "perturbations" in the early universe. Since the Friedmann equations assume homogeneity, additional theory must be added before comparison to experiments. [[Inflation (cosmology)|Inflation]] is a simple model producing perturbations by postulating an extremely rapid expansion early in the universe that separates quantum fluctuations before they can equilibrate. The perturbations are characterized by additional parameters also determined by matching observations.<ref name=PDG-2024/>{{rp|25.1.2}}

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}}</ref>

The model includes a single originating event, the "[[Big Bang]]", which was not an explosion but the abrupt appearance of expanding [[spacetime]] containing radiation at temperatures of around 10¹⁵&nbsp;K. This was immediately (within 10⁻²⁹ seconds) followed by an exponential expansion of space by a scale multiplier of 10²⁷ or more, known as [[cosmic inflation]]. The early universe remained hot (above 10 000 K) for several hundred thousand years, a state that is detectable as a residual [[cosmic microwave background]], or CMB, a very low-energy radiation emanating from all parts of the sky. The "Big Bang" scenario, with cosmic inflation and standard particle physics, is the only cosmological model consistent with the observed continuing expansion of space, the observed distribution of [[Big Bang nucleosynthesis|lighter elements in the universe]] (hydrogen, helium, and lithium), and the spatial texture of minute irregularities ([[Anisotropy|anisotropies]]) in the CMB radiation. Cosmic inflation also addresses the "[[horizon problem]]" in the CMB; indeed, it seems likely that the universe is larger than the observable [[particle horizon]].<ref>{{Cite journal |lastlast1=Davis |firstfirst1=Tamara M. |last2=Lineweaver |first2=Charles H. |date=January 2004 |title=Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe |url=https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/expanding-confusion-common-misconceptions-of-cosmological-horizons-and-the-superluminal-expansion-of-the-universe/EFEEEFD8D71E59F86DDA82FDF576EFD3 |journal=Publications of the Astronomical Society of Australia |language=en |volume=21 |issue=1 |pages=97–109 |doi=10.1071/AS03040 |issn=1323-3580|arxiv=astro-ph/0310808 |bibcode=2004PASA...21...97D }}</ref>

== Cosmic expansion history ==

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|+ Planck Collaboration Cosmological parameters

! &emsp;&emsp;

! Description<ref name="Planck-2013">The parameters used in the Planck series of papers are described in Table 1 of {{Cite journal |lastlast1=Ade |firstfirst1=P. a. R. |last2=Aghanim |first2=N. |last3=Armitage-Caplan |first3=C. |last4=Arnaud |first4=M. |last5=Ashdown |first5=M. |last6=Atrio-Barandela |first6=F. |last7=Aumont |first7=J. |last8=Baccigalupi |first8=C. |last9=Banday |first9=A. J. |last10=Barreiro |first10=R. B. |last11=Bartlett |first11=J. G. |last12=Battaner |first12=E. |last13=Benabed |first13=K. |last14=Benoît |first14=A. |last15=Benoit-Lévy |first15=A. |date=2014-11-01 |title=Planck 2013 results. XVI. Cosmological parameters |url=https://www.aanda.org/articles/aa/full_html/2014/11/aa21591-13/aa21591-13.html |journal=Astronomy & Astrophysics |language=en |volume=571 |pages=A16 |doi=10.1051/0004-6361/201321591 |issn=0004-6361|arxiv=1303.5076 |bibcode=2014A&A...571A..16P }}</ref>

! Symbol

! Value-2018<ref name="Planck 2018">

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* Prediction of the observed [[Polarization (cosmology)|B-mode polarization]] of the CMB light due to primordial gravitational waves.<ref name="Ade-BModes-2021">{{Cite journal |last1=Ade |first1=P. A. R. |last2=Ahmed |first2=Z. |last3=Amiri |first3=M. |last4=Barkats |first4=D. |last5=Thakur |first5=R. Basu |last6=Bischoff |first6=C. A. |last7=Beck |first7=D. |last8=Bock |first8=J. J. |last9=Boenish |first9=H. |last10=Bullock |first10=E. |last11=Buza |first11=V. |last12=Cheshire |first12=J. R. |last13=Connors |first13=J. |last14=Cornelison |first14=J. |last15=Crumrine |first15=M. |date=2021-10-04 |title=Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.151301 |journal=Physical Review Letters |language=en |volume=127 |issue=15 |page=151301 |doi=10.1103/PhysRevLett.127.151301 |pmid=34678017 |arxiv=2110.00483 |bibcode=2021PhRvL.127o1301A |issn=0031-9007}}</ref><ref name="Snowmass21"/>

* Observations of H₂O emission spectra from a galaxy 12.8 billion light years away consistent with molecules excited by cosmic background radiation much more energetic – 16-20K – than the CMB we observe now, 3K.<ref name="Riechers-2022">{{Cite journal |last1=Riechers |first1=Dominik A. |last2=Weiss |first2=Axel |last3=Walter |first3=Fabian |last4=Carilli |first4=Christopher L. |last5=Cox |first5=Pierre |last6=Decarli |first6=Roberto |last7=Neri |first7=Roberto |date=February 2022 |title=Microwave background temperature at a redshift of 6.34 from H2O absorption |journal=Nature |language=en |volume=602 |issue=7895 |pages=58–62 |doi=10.1038/s41586-021-04294-5 |issn=1476-4687 |pmc=8810383 |pmid=35110755}}</ref><ref name="Snowmass21"/>

* Predictions of the primordial abundance of [[deuterium]] as a result of [[Big Bang nucleosynthesis]].<ref name="Cooke-2014">{{Cite journal |lastlast1=Cooke |firstfirst1=Ryan J. |last2=Pettini |first2=Max |last3=Jorgenson |first3=Regina A. |last4=Murphy |first4=Michael T. |last5=Steidel |first5=Charles C. |date=2014-01-03 |title=PRECISIONPrecision MEASURESMeasures OFof THEthe PRIMORDIALPrimordial ABUNDANCEAbundance OFof DEUTERIUMDeuterium |journal=The Astrophysical Journal |volume=781 |issue=1 |pages=31 |doi=10.1088/0004-637x/781/1/31 |issn=0004-637X|arxiv=1308.3240 |bibcode=2014ApJ...781...31C }}</ref> The observed abundance matches the one derived from the nucleosynthesis model with the value for baryon density derived from CMB measurements.<ref name="Turner"/>{{rp|4.1.2}}

In addition to explaining many pre-2000 observations, the model has made a number of successful predictions: notably the existence of the [[baryon acoustic oscillation]] feature, discovered in 2005 in the predicted ___location; and the statistics of weak [[gravitational lensing]], first observed in 2000 by several teams. The [[Cosmic microwave background#Polarization|polarization]] of the CMB, discovered in 2002 by DASI,<ref>{{cite journal |last1=Kovac|first1=J. M.|last2=Leitch|first2=E. M.|last3=Pryke|first3=C.|author3-link=Clement Pryke|last4=Carlstrom|first4=J. E.|last5=Halverson|first5=N. W. |last6=Holzapfel |first6=W. L.|title=Detection of polarization in the cosmic microwave background using DASI |journal=Nature |year=2002|volume=420|issue=6917 |pages=772–787 |doi=10.1038/nature01269 |pmid=12490941 |arxiv=astro-ph/0209478|bibcode=2002Natur.420..772K|s2cid=4359884|url=https://cds.cern.ch/record/582473}}</ref> has been successfully predicted by the model: in the 2015 ''Planck'' data release,<ref>{{cite journal |title=Planck 2015 Results. XIII. Cosmological Parameters |arxiv=1502.01589 |author1=Planck Collaboration |year=2016 |doi=10.1051/0004-6361/201525830 |volume=594 |issue=13 |journal=Astronomy & Astrophysics |page=A13 |bibcode=2016A&A...594A..13P|s2cid=119262962 }}</ref> there are seven observed peaks in the temperature (TT) power spectrum, six peaks in the temperature–polarization (TE) cross spectrum, and five peaks in the polarization (EE) spectrum. The six free parameters can be well constrained by the TT spectrum alone, and then the TE and EE spectra can be predicted theoretically to few-percent precision with no further adjustments allowed.{{citation needed|date=February 2024}}