Moments of the Cluster Distribution as a Test of Dark Matter Models

We estimate the variance and the skewness of the cluster distribution in several dark matter (DM) models. The cluster simulations are based on the Zel’dovich approximation, the low computational cost of which allows us to run 50 random realizations of each model. We compare our results with those coming from a similar analysis of a redshift sample of Abell/ACO clusters. Within the list of the considered models, we find that only the model based on Cold+Hot DM (with ${\mathrm{\Omega }}_{\mathrm{h}\mathrm{o}\mathrm{t}}=0.3$) provides a good fit to the data. The standard CDM model and the low-density (${\mathrm{\Omega }}_{\circ }=0.2$) CDM models, both with and without a cosmological constant term (${\mathrm{\Omega }}_{\mathrm{\Lambda }}=0.8$) are ruled out. The tilted CDM model with primordial spectral index $n=0.7$ and a low Hubble constant ($h=0.3$) CDM model are only marginally consistent with the data.