Growth of correlations in gravitational N-body simulations

In the gravitational evolution of a cold infinite particle distribution, two-body interactions can be predominant at early times: we show that, by treating the simple case of a Poisson particle distribution in a static universe as an ensemble of isolated two-body systems, one may capture the origin of the first nonlinear correlated structures. The developed power-law-like behavior of the two-point correlation function is then simply related to the functional form of the time-evolved nearest-neighbor probability distribution, whose time dependence can be computed by using the Liouville theorem for the gravitational two-body problem. We then show that a similar dynamical evolution is also found in a large-scale ordered distribution, which has striking similarities to the case of a cosmological cold dark matter simulation which we also consider.