HIGHER-ORDER MOMENTS OF THE MATTER DISTRIBUTION IN SCALE-FREE COSMOLOGICAL SIMULATIONS WITH LARGE DYNAMIC-RANGE

We calculate reduced moments xi(q)BAR of the matter density fluctuations, up to order q = 5, from counts in cells produced by particle-mesh numerical simulations with scale-free Gaussian initial conditions. We use power-law spectra P(k) is-proportional-to k(n) with indices n = - 3, - 2, - 1, 0, 1. Due to the supposed absence of characteristic times or scales in our models, all quantities are expected to depend on a single scaling variable. For each model, the moments at all times can be expressed in terms of the variance xi2BAR, alone. We look for agreement with the hierarchical scaling ansatz, according to which xi(q)BAR is-proportional-to xi2q-1BAR. For n less-than-or-equal-to -2 models, we find strong deviations from the hierarchy, which are mostly due to the presence of boundary problems in the simulations. A small, residual signal of deviation from the hierarchical scaling is however also found in n greater-than-or-equal-to -1 models. The wide range of spectra considered and the large dynamic range, with careful checks of scaling and shot-noise effects allows us to reliable detect evolution away from the perturbation theory result.