21. The Cosmological Parameters 1

Rapid advances in observational cosmology are leading to the establishment of the first 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 anisotropies, led by the three-year results from the Wilkinson Microwave Anisotropy Probe (WMAP) [1,2]. 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 descriptions 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 decoupling. 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 Ωi for the various matter species and ΩΛ for the cosmological constant, the Friedmann equation can be written