Cosmological Solutions of Some Nonlocal Gravity Models

Despite of some significant phenomenological successes and many nice theoretical properties, General relativity (GR) is not complete theory of gravity. Hence, there are many attempts to modify GR. One of promising modern approaches towards more complete theory of gravity is nonlocal modification of GR. Our nonlocal gravity model is given by the action (without matter) $S = \frac{1}{16 \pi G}\int \sqrt{-g} (R - 2\Lambda + P(R) \mathcal{F}(\Box) Q(R)) d^4x ,$ where $R$ is scalar curvature and $\Lambda$ – cosmological constant. $P(R)$ and $Q(R)$ are some differentiable functions of $R$. $\mathcal{F}(\Box) = \sum_{n=0}^\infty f_n \Box^n$ is an analytic function of the dAlambertian $\Box .$ We present a brief review of some general properties, and cosmological solutions for some concrete functions $P(R)$ and $Q(R)$