The nonlinear matter power spectrum

We modify the public PM code developed by Anatoly Klypin and Jon Holtzman to simulate cosmologies with arbitrary initial power spectra and the equation of state of dark energy. With this tool in hand, we perform the following studies on the matter power spectrum. With an artificial sharp peak at k similar to 0.2 h Mpc(-1) in the initial power spectrum, we find that the position of the peak is not shifted by nonlinear evolution. An upper limit of the shift at the level of 0.02% is achieved by fitting the power spectrum local to the peak using a power law plus a Gaussian. We also find that the existence of a peak in the linear power spectrum would boost the nonlinear power at all scales evenly. This is contrary to what theHKLMscaling relation predicts, but roughly consistent with that of the halo model. We construct dark energy models with the same linear power spectra today but different linear growth histories. We demonstrate that their nonlinear power spectra differ at the level of the maximum deviation of the corresponding linear power spectra in the past. Similarly, two constructed dark energy models with the same growth histories result in consistent nonlinear power spectra. This is hinting, not a proof, that the linear power spectrum together with linear growth history uniquely determine the nonlinear power spectrum. Based on these results, we propose that linear growth history be included in the next-generation fitting formulae of the nonlinear power spectrum. Finally, we comment on the precision of existing fitting formulae when applied to dark energy models parametrized by w(0) and w(a).