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 Ω_ν = 0.2 contributed by two massive neutrinos (C + 2νDM), and a cold dark matter model with cosmological constant (ΛCDM) with Ω₀ = 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 P₀; and the underdensity probability function U_ɛ (where ɛ fixes the underdensity threshold in percentage of the average). We find that P₀ (for which PPS and CfA2 data agree) and P₁ distinguish efficiently between the models, while U_ɛ is only marginally discriminatory. On the contrary, the reduced skewness and kurtosis are, respectively, S₃ ~= 2.2 and S₄ ~= 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 + 2νDM in all the tests performed. In contrast, the above ΛCDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way.