Constraining the Power Spectrum using Clusters

(Shortened Abstract). We analyze a redshift sample of Abell/ACO clusters and compare them with numerical simulations based on the truncated Zel'dovich approximation (TZA), for a list of eleven dark matter (DM) models. For each model we run several realizations, on which we estimate cosmic variance effects. We analyse correlation statistics, the probability density function, and supercluster properties from percolation analysis. As a general result, we find that the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 < [-1.1,-0.9] are required by the Abell/ACO data. In order to obtain complementary constraints on the spectrum amplitude, we consider the cluster abundance as estimated using the Press--Schechter approach, whose reliability is explicitly tested against N--body simulations. We conclude that, of the cosmological models considered here, the only viable models are either Cold+Hot DM ones with Ømega_\nu = [0.2-0.3], better if shared between two massive neutrinos, and flat low-density CDM models with Ømega_0 = [0.3-0.5]