Cosmology of non-local f(R) gravity

Abstract

We consider a modification of GR with a special type of a non-local f (R). The structure of the non-local operators is motivated by the string field theory and p-adic string theory. The spectrum is derived explicitly and the ghost-free condition for the model is formulated. We pay special attention to the classical stability of the de Sitter solution in our model and formulate the conditions on the model parameters to have a stable configuration. Relevance of unstable configurations for the description of the de Sitter phase during inflation is specifically discussed.

Cosmological solutions of a nonlocal square root gravity

“…spin-2 modes remain the same as in general relativity with overall global constant factor renormalization at most. This follows from equations (57) and (58) for the second order variation of the action presented in [30]. For our most important solution, i.e.…”

“…In nonlocal gravity model (3), analytic function F(✷) is rather arbitrary -it is so far constrained only by a few conditions. Using procedure presented in our paper [30], one can show that there exists analytic function F(✷) with the de Sitter background without a ghost and tachyon, and will be presented elsewhere.…”

“…The following important remark follows from the analysis of physical excitations around the de Sitter background performed in [30], subsection 5.1. Our model (3) modifies only the scalar sector of perturbations, i.e.…”

“…The most attention has been paid to the case when P (R) = Q(R) = R, e.g. see [11,12,16,18,27,28,29,30,31,32,33,34].…”

Cosmological Solutions of Some Nonlocal Gravity Models

“…Concerning action (2), the most attention has been paid to the simple case when P (R) = Q(R) = R, e.g. see [10,11,17,18,20,29,30,31,32,33,34,35,36]. This investigation started in [10,11] by successful attempt to find nonsingular bouncing solution of the Big Bang singularity problem in standard cosmology.…”