21 . The Cosmological Parameters 1 21 . THE COSMOLOGICAL PARAMETERS

Rapid advances in observational cosmology have led to the establishment of a precision cosmological model, with many of the key cosmological parameters determined to one or two significant figure accuracy. Particularly prominent are measurements of cosmic microwave background (CMB) anisotropies, led by the seven-year results from the Wilkinson Microwave Anisotropy Probe (WMAP) [1–3]. However the most accurate model of the Universe requires consideration of a wide range of different types of observation, with complementary probes providing consistency checks, lifting parameter degeneracies, and enabling the strongest constraints to be placed. The term 'cosmological parameters' is forever increasing in its scope, and nowadays includes the parametrization of some functions, as well as simple numbers describing properties of the Universe. The original usage referred to the parameters describing the global dynamics of the Universe, such as its expansion rate and curvature. Also now of great interest is how the matter budget of the Universe is built up from its constituents: baryons, photons, neutrinos, dark matter, and dark energy. We need to describe the nature of perturbations in the Universe, through global statistical descriptors such as the matter and radiation power spectra. There may also be parameters describing the physical state of the Universe, such as the ionization fraction as a function of time during the era since recombination. Typical comparisons of cosmological models with observational data now feature between five and ten parameters. 21.1.1. The global description of the Universe : Ordinarily, the Universe is taken to be a perturbed Robertson–Walker space-time with dynamics governed by Einstein's equations. This is described in detail by Olive and Peacock in this volume. Using the density parameters Ω i for the various matter species and Ω Λ for the cosmological constant, the Friedmann equation can be written where the sum is over all the different species of material in the Universe. This equation applies at any epoch, but later in this article we will use the symbols Ω i and Ω Λ to refer to the present values. A typical collection would be baryons, photons, neutrinos, and dark matter (given charge neutrality, the electron density is guaranteed to be too small to be worth considering separately and is included with the baryons). The complete present state of the homogeneous Universe can be described by giving the current values of all the density parameters and of the Hubble parameter h. These also allow us to track the …