Statistical Tests for CHDM and ΛCDM Cosmologies

We apply several statistical estimators to high-resolution N-body simulationsof 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 ColdDark Matter model with Cosmological Constant (\LambdaCDM) with $\Omega_0=0.3$and h=0.7. Our aim is to compare simulated galaxy samples with thePerseus-Pisces redshift survey (PPS). We consider the n-point correlationfunctions (n=2-4), the N-count probability functions P_N, including the voidprobability 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 distinguishefficiently between the models, while U_\epsilon is only marginallydiscriminatory. 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 independentof the scale, in agreement with hierarchical scaling predictions and estimatesbased on redshift surveys. Among our results, we emphasize the remarkableagreement between PPS data and C+2\nuDM in all the tests performed. Incontrast, the above \LambdaCDM model has serious difficulties in reproducingobservational data if galaxies and matter overdensities are related in a simpleway.Comment: 12 pages, 10 figures, LaTeX (aaspp4 macro), in press on ApJ, Vol. 479, April 199