5.4. The amount of dark matter

In early papers on dark matter the total density due to visible and dark matter was estimated to be 0.2 of the critical cosmological density (Einasto, Kaasik & Saar 1974, Ostriker, Peebles & Yahil 1974). These estimates were based on the dynamics of galaxies in groups and clusters. In subsequent years several new independent methods were suggested. A direct method is based on the distant supernova project, which yields (for a spatially flat universe) _m = 0.28 ± 0.05 (Perlmutter et al. 1998, Riess 1998). Here and below density parameters are expressed in units of the critical cosmological density. Another method is based on X-ray data on clusters of galaxies, which gives the fraction of gas in clusters, f_gas = _b / _m. If compared to the density of the baryonic matter one gets the estimate of the total density, _m = 0.31 ± 0.05(h / 0.65)^-1/3 (Mohr et al. 2000). The evolution of the cluster abundance with time also depends on the density parameter (see Bahcall et al. 1999 for a review). This method yields an estimate _m = 0.4 ± 0.1 for the matter density. The formal weighted mean of these independent estimates is _m = 0.32 ± 0.03. This density value is close to the value _m = 0.3, suggested by Ostriker & Steinhardt (1995) as a concordant model.

More recently, the density parameter has been determined from clustering in the 2-degree Field Redshift Survey (Peacock et al. 2001), and from the angular power spectrum measurements of the cosmic microwave background radiation with the Wilkinson Microwave Anisotropy Probe (WMAP) (Spergel et al. 2003). The most accurate estimates of cosmological parameters are obtained using a combined analysis of the Sloan Digital Sky Survey and the WMAP data (Tegmark et al. 2003). According to this study the matter density parameter is _m = 0.30 ± 0.04. This method yields for the Hubble constant the value h = 0.70 ± 0.04 independent of other direct methods. From the same dataset the authors get for the density of baryonic matter, h² _b = 0.0232 ± 0.0012, which gives _b = 0.047 for the above value of the Hubble constant. Comparing both density estimates we get for the dark matter density _DM = _m - _b = 0.25.