Cluster surveys 335Figure 11.11. History of the star formation rate (SFR) in the universe (∼80% of the
cosmic time): SFR density versuss. redshift as derived by the UV luminosity density of
different distant galaxy samples (see Fergusonet al(2000) for a review). Loopback time
and distances are computed usingm,,h= 0. 3 , 0. 7 , 0 .65.
In this context, the cluster abundance at a given mass has long been
recognized as a stringent test for cosmological models. Typical rich clusters have
masses of about 5× 1014 h−^1 M , i.e. similar to the average mass within a sphere
of∼ 8 h−^1 Mpc radius in the unperturbed universe. Therefore, the local abundance
of clusters is expected to place a constraint onσ 8 , the rms mass fluctuation on the
8 h−^1 Mpc scale. Analytical arguments based on the approach devised by Press
and Schechter (1974) show that the cluster abundance is highly sensitive toσ 8
for a given value of the density parameterm. Once a model is tuned so as to
predict the correct abundance of local (z. 0 .1) clusters, its evolution will mainly
depend onm(e.g. Ekeet al1996). Therefore, by following the evolution of the
cluster abundance with redshift one can constrain the value of the matter density
parameter and the fluctuation amplitude level at the cluster scale.
The evolution of cosmic structures, building up in a process of hierarchical
clustering, is well illustrated in the VIRGO simulations (Jenkinset al1998)
of figure 11.12 (see also the chapter by Anatoly Klypin in this volume). The