Redshift Evolution of Galaxy Cluster Densities

The number of rich galaxy clusters per unit volume is a strong function of Omega, the cosmological density parameter, and sigma_8, the linear extrapolation to z=0 of the density contrast in 8/h Mpc spheres. The CNOC cluster redshift survey provides a sample of clusters whose average mass profiles are accurately known, which enables a secure association between cluster numbers and the filtered density perturbation spectrum. We select from the CNOC cluster survey those EMSS clusters with bolometric L_x>=10^45 erg/s and a velocity dispersion exceeding 800 km/s in the redshift ranges 0.18-0.35 and 0.35-0.55. We compare the number density of these subsamples with similar samples at both high and low redshift. Using the Press-Schechter formalism and CDM style structure models, the density data are described with sigma_8~0.85 and Omega~0.3, but Omega=0.2 and sigma_8=1.05+/-0.05 also are acceptable, as are other Omega<=0.6. The predicted cluster density evolution in an Omega=1 CDM model exceeds that observed by more than an order of magnitude.