The 3-point function in the large scale structure: I. The weakly non-linear regime in N-body simulations

Abstract

This paper presents a comparison of the predictions for the 2 and 3-point correlation functions of density fluctuations, xi_2 and xi_3, in gravitational perturbation theory (PT) against large Cold Dark Matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10 Mpc/h) thanks to the development of a new algorithm to estimate correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the 3-point statistics to simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as the ones presented here, were limited to small scales were leading order PT gives a poor approximation. Here we also propose and apply a method for separating the first and subsequent orders contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime were simulations do reproduce the leading order (tree-level) predictions of PT for the reduced 3-point function Q_3 ~ xi_3/ xi_2^2. For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ~ 20 Mpc/h. On larger scales xi_2 goes to zero and the results are dominated by sampling errors. In more realistic models (like the Lambda CDM cosmology) deviations from the leading order PT become important at smaller scales ~ 10 Mpc/h, although this depends on the particular 3-point configuration. (abridge)