Regularized cosmological power spectrum and correlation function in modified gravity models

Taruya A. (Yukawa Institute for Theoretical Physics Kyoto University (YITP), Kyoto 606-8502, JAPAN) Nishimichi T. (Institut d\'Astrophysique de Paris (IAP-CNRS), 98 bis Bld Arago, F-75014 Paris, FRANCE) Bernardeau F. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France) Hiramatsu T. (Yukawa Institute for Theoretical Physics Kyoto University (YITP), Kyoto 606-8502, JAPAN) Koyama K. (Institute of Cosmology & Gravitation, University of Portsmouth, Portsmouth PO1 2EG, England UNITED KINGDOM (UK))

Abstract: Based on the multi-point propagator expansion, we present resummed perturbative calculations for cosmological power spectra and correlation functions in the context of modified gravity. In a wide class of modified gravity models that have a screening mechanism to recover general relativity (GR) on small scales, we apply the eikonal approximation to derive the governing equation for resummed propagator that partly includes the non-perturbative effect in the high-k limit. The resultant propagator in the high-k limit contains the new corrections arising from the screening mechanism as well as the standard exponential damping. We explicitly derive the expression for new high-k contributions in specific modified gravity models, and find that in the case of f(R) gravity for a currently constrained model parameter, the corrections are basically of the sub-leading order and can be neglected. Thus, in f(R) gravity, similarly to the GR case, we can analytically construct the regularized propagator that reproduces both the resummed high-k behavior and the low-k results computed with standard perturbation theory, consistently taking account of the nonlinear modification of gravity valid at large scales. With the regularized multi-point propagators, we give predictions for power spectrum and correlation function at one-loop order, and compare those with N-body simulations in f(R) gravity model. As an important application, we also discuss the redshift-space distortions and compute the anisotropic power spectra and correlation functions.