Perturbation Theory Reloaded: Analytical Calculation of Nonlinearity in Baryonic Oscillations in the Real‐Space Matter Power Spectrum

Abstract

We compare the nonlinear matter power spectrum in real space calculated analytically from third-order perturbation theory with N -body simulations at 1 < z < 6. We find that the perturbation theory prediction agrees with the simulations to better than 1% accuracy in the weakly nonlinear regime in which the dimensionless power spectrum, Δ 2 ( k ) = k 3 P ( k )/2π 2 , which approximately gives the variance of the matter density field at a given k , is less than 0.4. While the baryonic acoustic oscillation features are preserved in the weakly nonlinear regime at z > 1, the shape of oscillations is distorted from the linear theory prediction. Nevertheless, our results suggest that one can correct the distortion caused by nonlinearity almost exactly . We also find that perturbation theory, which does not contain any free parameters, provides a significantly better fit to the simulations than the conventional approaches based on empirical fitting functions to simulations. Future work should include perturbation theory calculations of nonlinearity in redshift-space distortion and halo biasing in the weakly nonlinear regime.