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 from a compilation including the ESO Northern Abell Cluster Survey (ENACS) results in a significantly higher normalization for models, corresponding to $\sigma_8\approx 0.6$ for $\Omega_0=1$, compared to the Eke, Cole, & Frenk result of $\sigma_8=0.52\pm 0.04$. 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.