CONSTRAINING THE POWER SPECTRUM USING CLUSTERS

We analyze an extended redshift sample of Abell/ACO clusters and compa re the results with those coming from numerical simulations of the clu ster distribution, based on the truncated Zel'dovich approximation (TZ A), for a list of eleven dark matter (DM) models. For each model we ru n several realizations, so that we generate a set of 48 independent mo ck Abell/ACO cluster samples per model, on which we estimate cosmic va riance effects. Other than the standard CDM model, we consider (a) Ohm (0) = 1 CDM models based on lowering the Hubble parameter and/or on ti lting the primordial spectrum; (b) Ohm(0) = 1 Cold + Hot DM models wit h 0.1 less than or equal to Ohm(nu) less than or equal to 0.5; (c) low -density flat Lambda CDM models with 0.3 less than or equal to Ohm(0) less than or equal to 0.5. We compare real and simulated cluster distr ibutions by analysing correlation statistics, the probability density function, and supercluster properties from percolation analysis. We in troduce a generalized definition of the spectrum shape parameter Gamma in terms of sigma(25)/sigma(g), where sigma(r) is the rms fluctuation amplitude within a sphere of radius r. As a general result, we find t hat the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape par ameter 0.18 less than or similar to Gamma less than or similar to 0.25 and an effective spectral index at the 20 h(-1) Mpc scale -1.1 less t han or similar to n(eff) less than or similar to -0.9 are required by the Abell/ACO data. In order to obtain complementary constraints on th e spectrum amplitude, we consider the cluster abundance as estimated u sing the Press-Schechter approach, whose reliability is explicitly tes ted against N-body simulations. By combining results from the analysis of the distribution and the abundance of clusters we conclude that, o f the cosmological models considered here, the only viable models are either Cold + Hot DM ones with 0.2 less than or similar to Q(nu) less than or similar to 0.3, better if shared between two massive nu specie s, and Lambda CDM ones with 0.3 less than or similar to Ohm(0) less th an or similar to 0.5.