Editing Lambda-CDM model (section)

== Parameters ==
Multiple variants of the ΛCDM model are used with some differences in parameters.<ref name=PDG-2024/>{{rp|loc=25.1}} One such set is outlined in the table below. 
{| class="wikitable"
|+ 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 |last=Ade |first=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}}</ref>
! Symbol
! Value-2018<ref name="Planck 2018">
{{cite journal
 |author=Planck Collaboration
 |year=2020
 |title=Planck 2018 results. VI.&nbsp;Cosmological parameters
 |journal=Astronomy & Astrophysics
 |volume=641 |at=page&nbsp;A6 (see PDF page&nbsp;15, Table&nbsp;2: "Age/Gyr", last&nbsp;column)
 |doi=10.1051/0004-6361/201833910
 |arxiv=1807.06209 |bibcode=2020A&A...641A...6P
 |s2cid=119335614
}}</ref>
|-
! rowspan="6" {{vert header|&ensp;Independent parameters}}
| Baryon density today{{efn|name=physical density|The "physical baryon density parameter" Ω<sub>b</sub> {{var|h}}<sup>2</sup> is the "baryon density parameter" Ω<sub>b</sub> multiplied by the square of the reduced Hubble constant {{nowrap|1= {{var|h}} = {{var|H}}<sub>0</sub> / (100&nbsp;km⋅s<sup>−1</sup>⋅Mpc<sup>−1</sup>)}}.<ref>[https://web.archive.org/web/20120305082531/http://www.lsst.org/files/docs/sciencebook/SB_A.pdf Appendix A] of the [http://www.lsst.org/lsst/scibook LSST Science Book Version 2.0] {{Webarchive|url=https://web.archive.org/web/20130226112941/http://www.lsst.org/lsst/scibook |date=2013-02-26 }}</ref><ref>p. 7 of [https://web.archive.org/web/20140421213818/http://wfirst.gsfc.nasa.gov/science/fomswg/fomswg_technical.pdf Findings of the Joint Dark Energy Mission Figure of Merit Science Working Group]</ref> Likewise for the difference between "physical dark matter density parameter" and "dark matter density parameter".}}
| align="center" | Ω<sub>b</sub> {{var|h}}<sup>2</sup>
| {{val|0.0224|0.0001}}
|-
| Cold dark matter density today{{efn|name=physical density}}
| align="center" | Ω<sub>c</sub> {{var|h}}<sup>2</sup>
| {{val|0.120|0.001}}
|-
| 100 × approximation to r∗/DA (CosmoMC)
| align="center" | 100<math>\theta_{MC}</math>
| {{val|1.04089|0.00031}}
|-
| [[Reionization]] [[optical depth]]
| align="center" | {{var|τ}}
| {{val|0.054|0.007}}
|-
| Log power of the primordial curvature perturbations
| align="center" |<math>\ln(10^{10}A_s)</math>
| {{val|3.043| 0.014}}
|-
| Scalar spectrum power-law index 
| align="center" | {{var|n}}<sub>s</sub>
| {{val|0.965|0.004}}
|-
! rowspan="6" {{vert header|&ensp;&emsp;&emsp;Fixed parameters}}
| Total matter density today (inc. massive neutrinos
| align="center" | Ω<sub>m</sub> {{var|h}}<sup>2</sup>
| 0.1428 ± 0.0011
|-
| Equation of state of dark energy
| align="center" | {{var|w}}
| w<sub>0</sub> = −1
|-
| Tensor/scalar ratio
| align="center" | {{var|r}}
| r<sub>0.002</sub> <  0.06
|-
| Running of spectral index
| align="center" |<math>d n_\text{s} / d \ln k</math>
| 0
|-
| Sum of three neutrino masses
| align="center" |<math>\sum m_\nu</math>
| 0.06 [[electronvolt (mass)|eV/{{var|c}}{{sup|2}}]]
|-
| Effective number of relativistic degrees of freedom
| align="center" | ''N''<sub>eff</sub>
| {{val|2.99|0.17}}
|-
! rowspan="10" {{vert header|&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;Calculated Values}}
| [[Hubble constant]]
| align="center" | {{var|H}}<sub>0</sub>
| {{val|67.4|0.5|u=km⋅s<sup>−1</sup>⋅[[parsec|Mpc]]<sup>−1</sup>}}
|-
| [[Age of the universe]]
| align="center" | {{var|t}}<sub>0</sub>
| {{val|13.787|0.020|e=9}} years<ref name="Planck 2018age">
{{cite journal
 |author=Planck Collaboration
 |year=2020
 |title=Planck 2018 results. VI.&nbsp;Cosmological parameters
 |journal=Astronomy & Astrophysics
 |volume=641 |at=page&nbsp;A6 (see PDF page&nbsp;15, Table&nbsp;2: "Age/Gyr", last&nbsp;column)
 |doi=10.1051/0004-6361/201833910
 |arxiv=1807.06209 |bibcode=2020A&A...641A...6P
 |s2cid=119335614
}}
</ref>
|-
| [[Dark energy]] density parameter{{efn|name=density| Density parameters are expressed relative to a critical density {{var|ρ}}{{sub|crit}}, which is the total density of matter/energy needed for the universe to be spatially flat: {{nowrap|1=Ω{{sub|{{var|x}}}} = {{var|ρ}}{{sub|{{var|x}}}} / {{var|ρ}}{{sub|crit}}}}.<ref name=Peacock-1998>{{Cite book |last=Peacock |first=J. A. |url=https://www.cambridge.org/core/product/identifier/9780511804533/type/book |title=Cosmological Physics |date=1998-12-28 |publisher=Cambridge University Press |isbn=978-0-521-41072-4 |edition=1 |doi=10.1017/cbo9780511804533}}</ref>{{rp|74}}}}
| align="center" | Ω<sub>Λ</sub>
| {{val|0.6847|0.0073}}
|-
| The present root-mean-square matter fluctuation,<br>averaged over a sphere of radius 8''h''<sup>−1</sup> Mpc
| align="center" | {{var|σ}}<sub>8</sub>
| {{val|0.811|0.006}}
|-
| Redshift of reionization (with uniform prior)
| align="center" | {{var|z}}<sub>re</sub>

| {{val|7.68|0.79}}
|}
{{Clear}}
The [[Planck (spacecraft)|Planck]] collaboration version of the ΛCDM model is based on six [[parameter]]s: baryon density parameter; dark matter density parameter; scalar spectral index; two parameters related to curvature fluctuation amplitude; and the probability that photons from the early universe will be scattered once on route (called reionization optical depth).<ref name="Planck-2013"/> Six is the smallest number of parameters needed to give an acceptable fit to the observations; other possible parameters are fixed at "natural" values, e.g. total density parameter = 1.00, dark energy equation of state = −1.

The parameter values, and uncertainties, are estimated using computer searches to locate the region of parameter space providing an acceptable match to cosmological observations. From these six parameters, the other model values, such as the [[Hubble's law|Hubble constant]] and the [[dark energy]] density, can be calculated.

{{notelist}}