Statistical tests for CHDM and Lambda CDM 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 nu DM), and a cold dark matter model with cosmological constant (Lambda CDM) 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 similar or equal to 2.2 and S-4 similar or equal to 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 nu DM in all the tests performed. In contrast, the above Lambda CDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way.