**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,
*h*^{2}
_{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.