### abstract

- We report on analyses of cluster samples obtained from the Hubble Volume Simulations. These simulations, an $\Omega=1$ model named $\tau$CDM and a flat low $\Omega$ model with a cosmological constant ($\Lambda$CDM), comprise the largest computational efforts to date in numerical cosmology. We investigate the presence of massive galaxy clusters at $z\approx 0.8$. The $\tau$CDM model fails to form clusters at such a redshift. However, due to the small number of observed clusters around $z\approx 0.8$ 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 $\xi$. We show that the relationship between the mean density of subsamples of clusters, expressed via their mean separation $d_{\rm c}$, and the correlation length $r_0$, defined through $\xi(r_0) = 1$, is not linear but turns over gently for large $d_{\rm c}$. An analytic prediction by Mo & White (1996) overpredicts $r_0$. The results from the analysis of the APM cluster data by Croft et al. (1997) are nicely matched by the $\Lambda$CDM model.