Statistical Tests for CHDM and ΛCDM Cosmologies

We apply several statistical estimators to high-resolution N-body simulations of two currently viable cosmological models: a mixed dark matter model, having $\Omega_\nu=0.2$ contributed by two massive neutrinos (C+2\nuDM), and a Cold Dark Matter model with Cosmological Constant (\LambdaCDM) with $\Omega_0=0.3$ and h=0.7. Our aim is to compare simulated galaxy samples with the Perseus-Pisces redshift survey (PPS). We consider the n-point correlation functions (n=2-4), the N-count probability functions P_N, including the void probability function P_0, and the underdensity probability function U_\epsilon (where \epsilon fixes the underdensity threshold in percentage of the average). We find that P_0 (for which PPS and CfA2 data agree) and P_1 distinguish efficiently between the models, while U_\epsilon is only marginally discriminatory. On the contrary, the reduced skewness and kurtosis are, respectively, S_3\simeq 2.2 and S_4\simeq 6-7 in all cases, quite independent of the scale, in agreement with hierarchical scaling predictions and estimates based on redshift surveys. Among our results, we emphasize the remarkable agreement between PPS data and C+2\nuDM in all the tests performed. In contrast, the above \LambdaCDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way.