Galaxy Clusters in the Hubble Volume Simulations

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We report on analyses of cluster samples obtained from the Hubble Volume Simulations. These simulations, an Ω=1 model named τCDM and a flat low Ω model with a cosmological constant (ΛCDM), comprise the largest computational efforts to date in numerical cosmology. We investigate the presence of massive galaxy clusters at z≈ 0.8. The τCDM model fails to form clusters at such a redshift. However, due to the small number of observed clusters around z≈ 0.8 and the uncertainties in the determinations of their masses, this conclusion still is somewhat preliminary. We produce cluster catalogs at z=0 for both cosmologies and investigate their two--point correlation function ξ. We show that the relationship between the mean density of subsamples of clusters, expressed via their mean separation d c, and the correlation length r₀, defined through ξ(r₀) = 1, is not linear but turns over gently for large d c. An analytic prediction by Mo & White (1996) overpredicts r₀. The results from the analysis of the APM cluster data by Croft et al. (1997) are nicely matched by the ΛCDM model.