Cosmological Solutions of Some Nonlocal Gravity Models

Abstract

In this paper, we investigate a nonlocal modification of general relativity (GR) with actionf n ✷ n is an analytic function of the d'Alembertian ✷. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if Λ = 0, k = 0, and they have not analogs in Einsten's gravity with cosmological constant Λ. One of these two solutions is a(t) = A √ t e Λ 4 t 2 , that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one -a(t) = A e Λt 2 . For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator F (✷), which satisfies obtained necessary conditions.