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 pe rturbation theory and numerical N-body simulations for the evolution o f density fluctuations in a standard cold dark matter universe. The ev olution of the power spectrum of density perturbations and the two-poi nt correlation function are studied in the non-linear regime, in order to determine the range of validity of the perturbation theory approac h. We conclude that perturbation theory gives a good estimate of the f orm of the power spectrum as the density field becomes mildly non-line ar, correctly predicting a transfer of power from larger to smaller sc ales. We find excellent agreement between the simulation results and p erturbation theory on length-scales for which the variance of the dens ity fluctuations is less than or equal to unity. This agreement gradua lly breaks down as the variance increases above unity. We investigate the claim made by Couchman & Carlberg, that the standard cold dark mat ter (CDM) model can be reconciled with observation if the density fiel d is highly evolved. For a linear variance in the mass density field o f 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 ga laxy clustering measured from the APM Survey is improved when non-line ar 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, calculate d to second order in perturbation theory, is very nearly unity. For wa venumbers 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.