The Cosmic Distribution of Clustering

For a given statistic, A, the cosmic distribution function, Υ(Ã), is the probability of measuring a value à in a finite galaxy catalog. For statistics related to count-in-cells, such as factorial moments, Fk, the average correlation function, ξ, and cumulants, SN , the functions Υ(F̃k), Υ( ̃ ξ), and Υ(S̃N ) were measured in a large τCDM 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 (∆A), the cosmic error. The resulting detailed knowledge about the shape of Υ 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, (∆A/A) ≪ 1, function Υ is nearly Gaussian. When (∆A/A) approaches unity or is larger, function Υ(Ã) is increasingly skewed and well approximated by a lognormal distribution for A = Fk, or A = ξ. 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.