COSMOLOGICAL N-BODY SIMULATIONS WITH A TREE CODE - FLUCTUATIONS IN THE LINEAR AND NONLINEAR REGIMES

The evolution of gravitational systems is studied numerically in a cosmological context using a hierarchical tree algorithm with fully periodic boundary conditions. The simulations employ 262,144 particles, which are initially distributed according to scale-free power spectra, P(k) proportional to k(n), with n = -2, -1, 0, and 1. The subsequent evolution is followed in both flat and open universes. With this large number of particles, the discretized system can accurately model the linear phase. It is shown that the dynamics in the nonlinear regime depends on both the spectral index n and the density parameter OMEGA. In OMEGA = 1 universes, the evolution of the two-point correlation function-xi agrees well with similarity solutions for xi greater-than-or-similar-to 100 but its slope is steeper in open models with the same n.