Analytical Approximation to the Nonlinear Power Spectrum of Gravitational Clustering

Abstract

This paper presents an analytical formula that closely approximates the fully nonlinear power spectrum of matter fluctuations for redshift $z\approx 5$ to 0 over a wide range of cosmologically interesting flat models with varying matter density $\Omega_m$ and neutrino fraction $\Omega_\nu$. The functional form is motivated by analytical solutions in asymptotic regimes, but in order to obtain accurate approximations, the coefficients are calculated from fits to the nonlinear power spectrum computed from numerical simulations of four cosmological models. The transformation from the linear to nonlinear power spectrum depends on $\Omega_m, \Omega_\nu$, and time. A simple scaling rule is introduced, which greatly simplifies the construction of the functional form and allows the formula to depend directly on the rms linear mass fluctuation $\sigma_8$ instead of on an effective spectral index as in earlier work.