The Cosmic Distribution of Clustering

Abstract

For a given statistic, A, the cosmic distribution function, Upsilon(VA), is the probability of measuring a value VA in a finite galaxy catalog. For statistics related to count-in-cells, such as factorial moments, F_k, the average correlation function, xiav, and cumulants, S_N, the functions Upsilon(VF_k), Upsilon(Vxiav), and Upsilon(VS_N) were measured in a large tauCDM simulation. This N-body experiment simulates almost the full ``Hubble Volume'' of the universe, thus, for the first time, it allowed for an accurate analysis of the cosmic distribution function, and, in particular, of its variance (Delta A)^2, the cosmic error. The resulting detailed knowledge about the shape of Upsilon is crucial for likelihood analyses. The measured cosmic error agrees remarkably well with the theoretical predictions of Szapudi & Colombi (1996) and Szapudi, Bernardeau & Colombi (1998) in the weakly non-linear regime, while the predictions are slightly above the measurements in the highly nonlinear regime. When the relative cosmic error is small, (Delta A/A)^2, function Upsilon is nearly Gaussian. When (Delta A/A)^2 approaches unity or is larger, function Upsilon(VA) is increasingly skewed and well approximated by a lognormal distribution for A=F_k, or A=xiav. The measured cumulants follow accurately the perturbation theory predictions in the weakly nonlinear regime. Extended perturbation theory is an excellent approximation for all the available dynamic range.