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 Ων = 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 PN, including the void probability function P0; and the underdensity probability function Uϵ (where ϵ 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 Uϵ 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.