Power-Law Correlation and Discreteness in Cosmological [ITAL]N[/ITAL]-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 ⟨Λ 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 ⟨Λ i ⟩) are thus essential in the development of these correlations.