Parameters
The ΛCDM model is based on six parameters: physical baryon density, physical dark matter density, dark energy density, scalar spectral index, curvature fluctuation amplitude and reionization optical depth. In accordance with Occam's razor, six is the smallest number of parameters needed to give an acceptable fit to current observations; other possible parameters are fixed at "natural" values e.g. total density = 1.00, dark energy equation of state = -1, neutrino masses are small enough to be negligible. (See below for extended models which allow these to vary).
The values of these six parameters are mostly not predicted by current theory (though, ideally, they may be related by a future "Theory of Everything"); except that most versions of cosmic inflation predict the scalar spectral index should be slightly smaller than 1, consistent with the estimated value 0.96. The parameter values, and uncertainties, are estimated using large computer searches to locate the region of parameter space providing an acceptable match to cosmological observations. From these six parameters the other model values, including the Hubble constant and age of the universe, can be readily calculated.
Commonly, the set of observations fitted includes the cosmic microwave background anisotropy, the brightness/redshift relation for supernovae, and large-scale galaxy clustering including the baryon acoustic oscillation feature. Other observations such as the Hubble constant, the abundance of galaxy clusters, weak gravitational lensing, globular cluster ages, are generally consistent with these, providing a check of the model, but are less accurately measured at present.
Parameter values listed below are from the Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) temperature and polarization observations. These include estimates based on data from Baryon Acoustic Oscillations and Type Ia supernova luminosity/time dilation measurements. Implications of the data for cosmological models are discussed in Komatsu et al. and Spergel et al.
| Parameter | Value | Description |
|---|---|---|
| t0 | years | Age of the universe |
| H0 | km s−1 Mpc−1 | Hubble constant |
| Ωbh2 | Physical baryon density | |
| Ωch2 | Physical dark matter density | |
| Ωb | Baryon density | |
| Ωc | Dark matter density | |
| ΩΛ | Dark energy density | |
| ΔR2 | , k0 = 0.002Mpc−1 | Curvature fluctuation amplitude |
| σ8 | Fluctuation amplitude at 8h−1Mpc | |
| ns | Scalar spectral index | |
| z* | Redshift at decoupling | |
| t* | years | Age at decoupling |
| τ | Reionization optical depth | |
| zreion | Redshift of reionization |
The "physical baryon density" Ωbh2 differs from the "baryon density" Ωb in that the baryon density gives the fraction of the critical density made up of baryons (the critical density is the total density of matter/energy needed for the universe to be spatially flat, with measurements indicating that the actual total density Ωtot is very close if not equal to this value, see below), while the physical baryon density is equal to the baryon density multiplied by the square of the reduced Hubble constant h, where h is related to the Hubble constant H0 by the equation H0 = 100 h (km/s)/Mpc. Likewise for the difference between "physical dark matter density" and "dark matter density".
Read more about this topic: Lambda-CDM Model
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