Cosmology of Nonlocal Gravity

Branko Dragovich

University of Belgrade,

Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

23.04.2018

General relativity is Einstein theory of gravity, which is successful at many scales, but still has not been verified for the universe as a whole. Hence there are many attempts to modify Einstein gravity with intention to describe accelerating expansion of the universe without dark energy and initial singularity. One of the recent and promising approaches is nonlocal modified gravity. Our nonlocal gravity is given by the action $S = \frac{1}{16 \pi G}\int \sqrt{-g} (R - 2\Lambda + P(R) \mathcal{F}(\Box) Q(R)) d^4x ,$ where $R$ is scalar curvature and $\Lambda$ -- cosmological constant. $P(R)$ and $Q(R)$ are some differentiable functions of $R$. $\mathcal{F}(\Box) = \sum_{n=1}^\infty f_n \Box^n$ is an analytic function of the d'Alambertian $\Box .$ We present some general properties of this nonlocal model as well as cosmological solutions for some concrete functions $P(R)$ and $Q(R) .$