Non-linear Evolution of Baryon Acoustic Oscillations from Improved Perturbation Theory in Real and Redshift Spaces

Atsushi Taruya, Takahiro Nishimichi, Shun Saito, Takashi Hiramatsu

Published 2009-06-02, updated 2009-11-25Version 2

We study the non-linear evolution of baryon acoustic oscillations in the matter power spectrum and correlation function from the improved perturbation theory (PT). Based on the framework of renormalized PT, we apply the {\it closure approximation} that truncates the infinite series of loop contributions at one-loop order, and obtain a closed set of integral equations for power spectrum and non-linear propagator. The resultant integral expressions keep important non-perturbative properties which can dramatically improve the prediction of non-linear power spectrum. Employing the Born approximation, we then derive the analytic expressions for non-linear power spectrum and the predictions are made for non-linear evolution of baryon acoustic oscillations in power spectrum and correlation function. A detailed comparison between improved PT results and N-body simulations shows that a percent-level agreement is achieved in a certain range in power spectrum and in a rather wider range in correlation function. Combining a model of non-linear redshift-space distortion, we also evaluate the power spectrum and correlation function in correlation function. In contrast to the results in real space, the agreement between N-body simulations and improved PT predictions tends to be worse, and a more elaborate modeling for redshift-space distortion needs to be developed. Nevertheless, with currently existing model, we find that the prediction of correlation function has a sufficient accuracy compared with the cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3 at z>=0.5.