On the problem of initial conditions in cosmological N-body simulations

Cosmological N-body simulations aim to calculate the non-linear gravitational growth of structures via particle dynamics. A crucial problem concerns the setting-up of the initial particle distribution, as standard theories of galaxy formation predict the properties of the initial continuous density field with small-amplitude correlated Gaussian fluctuations. The discretisation of such a field is a complex issue and particle fluctuations are especially relevant at small scales where non-linear dynamics firstly takes place. In general, most of the procedures which may discretise a continuous field give rise to Poisson noise, which would then dominate the non-linear small-scale dynamics due to nearest-neighbours interactions. In order to avoid such a noise, and to consider the dynamics as due only to large-scale (smooth) fluctuations, an ad hoc method (lattice or glassy system plus correlated displacements) has been introduced and used in cosmological simulations. We show that such a method gives rise to a particle distribution which does not have any of the correlation properties of the theoretical continuous density field. This is because discreteness effects, different from Poisson noise but nevertheless very important, determine particle fluctuations at any scale, making it completely different from the original continuous field. We conclude that discreteness effects play a central role in the non-linear evolution of N-body simulations.