  We modify the public PM code developed by Anatoly Klypin and Jon Holtzman to
simulate cosmology with arbitrary initial power spectrum and 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~0.2 h/Mpc in the initial power spectrum,
we find that the position of the peak is not shifted by nonlinear evolution. 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 HKLM scaling
relation predicts, but roughly consistent with that of halo model.
  We construct two 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 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 formulas of nonlinear power spectrum. (abridged)
