Regularized cosmological power spectrum and correlation function in
  modified gravity models
  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.
