Experimental cosmic statistics - I. Variance

Counts-in-cells are measured in the tau CDM Virgo Hubble Volume simulation. This large N-body experiment has 10(9) particles in a cubic box of size 2000 h(-1) Mpc. The unprecedented combination of size and resolution allows, for the first time, a realistic numerical analysis of the cosmic errors and cosmic correlations of statistics related to counts-in-cells measurements, such as the probability distribution function P-N itself, its factorial moments F-k and the related cumulants xi macr and S(N)s. These statistics are extracted from the whole simulation cube, as well as from 4096 subcubes of size 125 h(-1) Mpc, each representing a virtual random realization of the local universe. The measurements and their scatter over the subvolumes are compared to the theoretical predictions of Colombi, Bouchet & Schaeffer for P-0, and of Szapudi & Colombi and Szapudi, Colombi & Bernardeau for the factorial moments and the cumulants. The general behaviour of experimental variance and cross-correlations as functions of scale and order is well described by theoretical predictions, with a few per cent accuracy in the weakly non-linear regime for the cosmic error on factorial moments. On highly non-linear scales, however, all variants of the hierarchical model used by SC and SCB to describe clustering appear to become increasingly approximate, which leads to a slight overestimation of the error, by about a factor of two in the worst case. Because of the needed supplementary perturbative approach, the theory is less accurate for non-linear estimators, such as cumulants, than for factorial moments. The cosmic bias is evaluated as well, and, in agreement with SCB, is found to be insignificant compared with the cosmic variance in all regimes investigated. While higher order statistics were previously evaluated in several simulations, this work presents textbook quality measurements of S(N)s, 3 less than or equal to N less than or equal to 10, in an unprecedented dynamic range of 0.05 less than or similar to xi macr less than or similar to 50. In the weakly non-linear regime the results confirm previous findings and agree remarkably well with perturbation theory predictions including the one-loop corrections based on spherical collapse by Fosalba & Gaztanaga. Extended perturbation theory is confirmed on all scales.