Cosmological Solutions of Some Nonlocal Gravity Models

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 \(S=(16 \pi G)^{-1} \int \sqrt{-g}(R-2 \Lambda+P(R) \mathcal{F}(\square) Q(R)) d^{4} x\), where R is the scalar curvature, Γ is the cosmological constant, P(R) and Q(R) are some differentiable functions of R, and \(\mathcal{F}(\square)=\sum\nolimits_{n=1}^{+\infty} f_{n} \square^{n}\) 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).