The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

Abstract

ABSTRA C T This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, j and z, 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 h 21 Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function Q3 , z/j 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 21 . On larger scales j goes to zero and the results are dominated by sampling errors. In more realistic models (such as the LCDM cosmology) deviations from the leading-order PT become important at smaller scales r . 10 Mpc h 21 , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.