Cosmological Solutions of Some Nonlocal Gravity Models

Abstract

Significant phenomenological success and nice theoretical properties of general relativity (GR) are well known. However, GR is not a complete theory of gravity. Hence, there are many attempts to modify GR. One of the current approaches to a more complete theory of gravity is a nonlocal modification of GR. The nonlocal gravity approach, which we consider here without matter, is based on the action S=(16πG)−1∫−g(R−2Λ+P(R)ℱ(□)Q(R))d4x, where R is the scalar curvature, Γ is the cosmological constant, P(R) and Q(R) are some differentiable functions of R, and ℱ(□)=∑n=1+∞fn□n is an analytic function of the corresponding d’Alembert operator □. We present here a brief review of some general properties and cosmological solutions for some specific functions P(R) and Q(R).