Lambda-CDM model

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A pie chart indicating the proportional composition of different energy-density components of the universe. Roughly ninety-five percent is  exotic dark matter and  dark energy.

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ΛCDM or  Lambda-CDM is  an abbreviation for Lambda-Cold Dark Matter. it  represents the current concordance model of big bang cosmology that explains cosmic microwave background observations, as well as large scale structure observations and  supernovae observations of the accelerating expansion of the universe. it  is the simplest known model that is  in general agreement with observed phenomena.

• Λ (Lambda) stands for the cosmological constant which is  a dark energy term that allows for the current accelerating expansion of the universe. The cosmological constant is  often described in terms of Ω_Λ, the fraction of the energy density of a flat Universe in the form of the cosmological constant. Currently, , implying 74% of the energy density of the present universe is  in this form.

• Cold dark matter is  the model where the dark matter is  explained as being cold (i.e. not thermalized), non-baryonic, collisionless dust. This component makes up 22% of the energy density of the present universe. The remaining 4% is  all of the matter and  energy that makes up the atoms and  photons that are  the building blocks of planets, stars, and  gas clouds in the universe.

• The model assumes a nearly scale-invariant spectrum of primordial perturbations and  a universe without spatial curvature. it  also assumes that it  has no observable topology, so that the universe is  much larger than the observable particle horizon. These are  predictions of cosmic inflation.

These are  the simplest assumptions for a consistent, physical model of cosmology. However, ΛCDM is  a model. Cosmologists anticipate that all of these assumptions will not be borne out exactly, after more  is learned about the applicable fundamental physics. In particular, cosmic inflation predicts spatial curvature at the level of 10⁻⁴ to 10⁻⁵. it  would also be surprising if the temperature of dark matter were absolute zero. Moreover, ΛCDM says nothing about the fundamental physical origin of dark matter, dark energy and  the nearly scale-invariant spectrum of primordial curvature perturbations: in that sense, it  is merely a useful parameterization of ignorance.

[edit] Parameters

The model has six parameters. The Hubble constant determines the rate of expansion of the universe, as well as the critical density for closure of the universe, ρ₀. Densities for baryons, dark matter and  dark energy are  given as Ωs, which are  the ratio of the true density to the critical density: e.g. Ω_b = ρ_b / ρ₀. Since the ΛCDM model assumes a flat universe, these densities sum to one, and  the density of dark energy is  not a free parameter. The optical depth to reionization determines the red shift of reionization. Information about the density fluctuations is  determined by the amplitude of the primordial fluctuations (from cosmic inflation) and  the spectral index, which measures how the fluctuations change with scale (n_s = 1 corresponds to a scale-invariant spectrum).

The errors quoted are  1σ: that is, there is  statistically a 68% likelihood that the true value falls within the upper and  lower error bounds. The errors are  not Gaussian, and  they have  been derived using a Markov chain Monte Carlo analysis by the Wilkinson Microwave Anisotropy Probe collaboration (Spergel et al. 2006) which also uses Sloan Digital Sky Survey and  Type Ia supernova data.

Parameter	Value	Description
Basic parameters
H0	km s-1 Mpc-1	Hubble parameter
Ωb		Baryon density
Ωm		Total matter density (baryons + dark matter)
τ		Optical depth to reionization
As		Scalar fluctuation amplitude
ns		Scalar spectral index
Derived parameters
ρ0	kg/m3	Critical density
ΩΛ		Dark energy density
zion		Reionization red-shift
σ8		Galaxy fluctuation amplitude
t0	years	Age of the universe

[edit] Extended models

Possible extensions of the simplest "vanilla" ΛCDM model are  to allow quintessence rather than a cosmological constant. In this case, the equation of state of dark energy is  different from −1. Cosmic inflation predicts tensor fluctuations (gravitational waves). Their amplitude is  parameterized by the tensor-to-scalar ratio, which is  determined by the energy scale of inflation. Other modifications allow for spatial curvature or  a running spectral index, which are  generally viewed as inconsistent with cosmic inflation.

Allowing these parameters will generally increase the errors in the vanilla parameters quoted above, and  may also shift the observed values somewhat.

Parameter	Value	Description
w		Equation of state
r	< 0.55 (2σ)	Tensor-to-scalar ratio
Ωk		Spatial curvature
α		Running of the spectral index
Σmν	< 0.87 eV (2σ)	Summed neutrino masses

These are  consistent with a cosmological constant, w = − 1, and  no spatial curvature Ω_k = 0. There is  some evidence for a running spectral index, but it  is not statistically significant. Theoretical expectations suggest that the tensor-to-scalar ratio r should be between 0 and  0.3, and  so should be tested in the near future.

[edit] References

• D. N. Spergel et al. (WMAP collaboration) (March 2006). "Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology".
• M. Tegmark et al. (SDSS collaboration), Cosmological Parameters from SDSS and  WMAP, Phys. Rev. D69 103501 (2004).
• D. N. Spergel et al. (WMAP collaboration), First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters, Astrophys. J. Suppl. 148 175 (2003).
• R. Rebolo et al. (VSA collaboration), Cosmological parameter estimation using Very Small Array data out to l=1500, Monthly Notices of the Royal Astronomical Society, Volume 353, Issue 3, pp. 747-759
• J. P. Ostriker and  P. J. Steinhardt, Cosmic Concordance, arXiv:astro-ph/9505066.