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 fluctuatio ns, 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 s ingle scaling variable. For each model, the moments at all times can b e expressed in terms of the variance xi2BAR, alone. We look for agreem ent 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, w e find strong deviations from the hierarchy, which are mostly due to t he presence of boundary problems in the simulations. A small, residual signal of deviation from the hierarchical scaling is however also fou nd 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 fr om the perturbation theory result.