Clusters in Various Cosmological Models: Abundance and Evolution

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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 Ω₀ with little contribution from other cosmological parameters. We investigate the significance of recent claims that this evolution indicates that Ω₀ 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 σ₈≈ 0.6 for Ω₀=1, compared to the Eke, Cole, & Frenk result of σ₈=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 Ω₀=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 Ω₀ unambiguously.