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(-1) Mpc spheres. The Canadian Network for Observational Cosmology (CNOC) cluster redshift survey provides a sample of clusters, the average mass profiles of which 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 Extended Medium-Sensitivity Survey clusters with bolometric L(x) greater than or equal to 10(45) ergs s(-1) and a velocity dispersion exceeding 800 km s(-)1 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 cold dark matter (CDM) style structure models, the density data are best described with sigma(8) similar or equal to 0.75 +/- 0.1 and Omega similar or equal to 0.4 +/- 0.2 (90% confidence). The duster dynamical analysis gives Omega = 0.2 +/- 0.1 for which sigma(8) = 0.95 +/- 0.1 (90% confidence). The predicted cluster density evolution in an Omega = 1 CDM model exceeds that observed by more than 1 order of magnitude.