Universality of power law correlations in gravitational clustering

¹ LPT, Université Paris-XI, Bâtiment 211 - F-91405 Orsay Cedex, France
² Département de Physique Théorique, Université de Genève 24 Quai E. Ansermet, CH-1211 Genève, Switzerland
³ LPNHE, Université de Paris VI - 4 Place Jussieu, Tour 33- RdC 75252 Paris Cedex 05, France

Received: 6 September 2002
Accepted: 16 February 2004

Abstract

We present an analysis of different sets of gravitational N-body simulations, all describing the dynamics of discrete particles with a small initial velocity dispersion. They encompass very different initial particle configurations, different numerical algorithms for the computation of the force, with or without the space expansion of cosmological models. Despite these differences we find in all cases that the non-linear clustering which results is essentially the same, with a well-defined simple power law behaviour in the two-point correlations in the range from a few times the lower cut-off in the gravitational force to the scale at which fluctuations are of order one. We argue, presenting quantitative evidence, that this apparently universal behaviour can be understood by the domination of the small-scale contribution to the gravitational force, coming initially from nearest-neighbor particles.