Power-law correlation and discreteness in cosmological N-body simulations

We analyse with simple real-space statistics the Virgo consortium's cosmological N-body simulations. Significant clustering rapidly develops well below the initial mean interparticle separation \Lambda_i, where the gravitational force on a particle is dominated by that with its nearest neighbours. A power-law behaviour in the two point correlation function emerges, which in the subsequent evolution is continuously amplified and shifted to larger scales, in a roughly self-similar manner. We conclude that the density fluctuations at the smallest scales due to the particle-like nature of the distribution being evolved are thus essential in the development of these correlations, and not solely, as usually supposed, the very small continuous (fluid-like) fluctuations at scales larger than \Lambda_i >.