Dependence of the non-linear mass power spectrum on the equation of state of dark energy

We present N-body simulation calculations of the dependence of the power spectrum of non-linear cosmological mass density fluctuations on the equation of state of the dark energy, w=p/rho. At fixed linear theory power, increasing w leads to an increase in non-linear power, with the effect increasing with k. By k=10 h/Mpc, a model with w=-0.75 has ~12% more power than a standard cosmological constant model (w=-1), while a model with w=-0.5 has ~33% extra power (at z=0). The size of the effect increases with increasing dark energy fraction, and to a lesser extent increasing power spectrum normalization, but is insensitive to the power spectrum shape (the numbers above are for Omega_m=0.281 and sigma_8=0.897). A code quantifying the non-linear effect of varying w, as a function of k, z, and other cosmological parameters, which should be accurate to a few percent for k<10 h/Mpc for models that fit the current observations, is available at http://www.cita.utoronto.ca/~pmcdonal/code.html. This paper also serves as an example of a detailed exploration of the numerical convergence properties of ratios of power spectra for different models, which can be useful because some kinds of numerical error cancel in a ratio. When precision calculations based on numerical simulations are needed for many different models, efficiency may be gained by breaking the problem into a calculation of the absolute prediction at a central point, and calculations of the relative change in the prediction with model parameters.