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

With simple real-space statistics, we analyze 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 its nearest neighbor contribution. A power-law behavior 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, due to the particle-like nature of the distribution being evolved, the density fluctuations at the smallest scales (not just, as usually supposed, the very small continuous [fluid-like] fluctuations at scales larger than [Lambda(i)]) are thus essential in the development of these correlations.