A COMPARISON OF THE EVOLUTION OF DENSITY FIELDS IN PERTURBATION-THEORY AND NUMERICAL SIMULATIONS .1. NONLINEAR EVOLUTION OF THE POWER SPECTRUM

We present a detailed comparison of the predictions of second-order perturbation theory and numerical N-body simulations for the evolution of density fluctuations in a standard cold dark matter universe. The evolution of the power spectrum of density perturbations and the two-point correlation function are studied in the non-linear regime, in order to determine the range of validity of the perturbation theory approach. We conclude that perturbation theory gives a good estimate of the form of the power spectrum as the density field becomes mildly non-linear, correctly predicting a transfer of power from larger to smaller scales. We find excellent agreement between the simulation results and perturbation theory on length-scales for which the variance of the density fluctuations is less than or equal to unity. This agreement gradually breaks down as the variance increases above unity. We investigate the claim made by Couchman & Carlberg, that the standard cold dark matter (CDM) model can be reconciled with observation if the density field is highly evolved. For a linear variance in the mass density field of 1.25, when measured in spheres of radius 8 h-1 Mpc, we find that the agreement between the standard CDM model and the power spectrum of galaxy clustering measured from the APM Survey is improved when non-linear effects are included for wavenumbers k less-than-or-equal-to 0.11 h Mpc-1. The variance in the mass fluctuations on this scale, calculated to second order in perturbation theory, is very nearly unity. For wavenumbers k > 0.11 h Mpc-1, a scale-dependent biasing scheme would be required, in order to match a standard CDM model with observations of the galaxy distribution.