Clusters in Various Cosmological Models: Abundance and Evolution

The combination of measurements of the local abundance of rich clusters of galaxies and its evolution to higher redshift offers the possibility of a direct measurement of Omega(0) with little contribution from other cosmological parameters. We investigate the significance of recent claims that this evolution indicates that Omega(0) must be small. The most recent cluster velocity dispersion function(1) from a compilation including the ESO Northern Abell Cluster Survey (ENACS) results in a significantly higher normalization for models, corresponding to sigma(8) approximate to 0.6 for Omega(0) = 1, compared to the Eke, Cole, & Frenk(2) result of sigma(8) = 0.52 +/- 0.04. Using the ENACS data for a z = 0 calibration results in strong evolution in the abundance of clusters, and we find that the velocity dispersion function is consistent with Omega(0) = 1. The results are dependent upon the choice and analysis of low-redshift and high-redshift data, so at present, the data is not good enough to determine Omega(0) unambiguously.