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

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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, Δ2(k) = k3P(k)/2π2, 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.