Astrophysics (Index)About

Lambda-CDM model

(ΛCDM, LCDM, standard model)
(Big-Bang cosmological model with a cosmological constant and cold dark matter)

The Lambda-CDM model (ΛCDM or LCDM) is a current, widely-used "working model" (standard model) of Big Bang/dark matter/dark energy cosmology. It includes cold dark matter and presumes a cosmological constant (Lambda aka Λ) in Einstein's field equation. The cosmological constant provides an explanation for the universe's observed accelerating expansion. The dark matter provides an explanation for the dynamics of galaxies and galaxy clusters that appear to have more gravitational attraction than their EMR can explain. (Other explanations for these phenomena include deviations in the behavior of gravity and/or dynamics from accepted models.) Lambda-CDM relates many observed phenomena to six apparently arbitrary parameters. Some values determined in 2015 using Planck observation data:

parametersymboldetermined value
physical baryon densityΩb0.02230
physical dark matter densityΩd0.1188
age of the universet013.799 × 109 years
scalar spectral indexns0.9667
curvature fluctuation amplitudeΔ²R2.441 × 10-9
optical depth to the epoch of reionization (EOR)τ0.066

(Values from other determinations do not match these exactly, but the differences are small.) These are not constants but are the current values for quantities that slowly shift with the passage of time (which is obvious for "age of the universe"). The six parameters cited may not be those listed above, but in combination, they would be equivalent to the above through relations assumed by the model. For example, the optical depth to reionization represents a measure of how long ago the EOR took place, which is sometimes indicated by the redshift of reionization (z ~ 11). h (in above) indicates the (dimensionless) Hubble parameter, which is the universe's expansion expressed as a fraction of 100 km s-1Mpc-1, which varies with time. Some additional values calculable from the six:

itemsymbolcalculated value
Hubble constantH067.74 km s-1Mpc-1
baryon density parameterΩb0.0486
dark matter density parameterΩd0.2589
matter density parameterΩm0.3089
dark energy density parameterΩΛ0.6911

The density parameters are expressed as fractions of the critical density. The dark matter density parameter is sometimes cited as Ωc, presumably for cold dark matter, but that symbol is also sometimes used to refer to the critical density parameter.


(astrophysics,model,cosmology,dark matter)
Further reading:
https://en.wikipedia.org/wiki/Lambda-CDM_model
https://lambda.gsfc.nasa.gov/education/graphic_history/univ_evol.cfm
https://ui.adsabs.harvard.edu/abs/2016A%26A...594A..13P/abstract
https://ui.adsabs.harvard.edu/abs/2020A%26A...641A...6P/abstract
https://ui.adsabs.harvard.edu/abs/2014A%26A...571A..16P/abstract
https://arxiv.org/abs/2201.08666
https://ui.adsabs.harvard.edu/abs/2024A%26A...682A..37T/abstract

Referenced by pages:
alternative cosmologies
angular power spectrum
astronomical quantities
Bolshoi simulation
cold dark matter (CDM)
Copernicus Complexio (COCO)
core-cusp problem
cosmological constant (Λ)
cosmological equation of state
cosmological model
cosmological simulation
cosmology
D56
dark energy (Λ)
dark matter (DM)
dark matter halo
dwarf galaxy problem
Einstein-de Sitter model
epoch of galaxy formation
fiducial
galaxy formation
Hubble tension
initial fluctuations
missing baryon problem
Planck
redshift-angular size relation
sigma-8 tension (S8 tension)
standard model
structure formation
wCDM

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