## International Conference on $p$-ADIC MATHEMATICAL PHYSICS AND ITS APPLICATIONS $p$-ADICS.2015, 07-12.09.2015, Belgrade, Serbia

Ivan Dimitrijević

### Nonlocal Modified Gravity

Abstract

After discovery of accelerating expansion of the Universe, there has been a renewed interest in gravity modification. One of promising approaches is nonlocal modification with the scalar curvature $R$ in the action replaced by a suitable function $F (R, \Box),$ where $\Box = \frac{1}{\sqrt{-g}}\partial_{\mu} \sqrt{-g} g^{\mu\nu} \partial_{\nu}$ is the Laplace-Beltrami operator. In particular we analyze the modification in the form \begin{equation*} S = \displaystyle \int \sqrt{-g}\Big(\frac{R}{16 \pi G} + R^{-1} \mathcal{F}(\Box)R \Big) \mathrm d^{4}x, \end{equation*} where $\mathcal{F} (\Box)$ is an analytic function, see [1], [2]. Derivations of EOM will be presented.

This is joint work with Branko Dragovich, Jelena Grujic and Zoran Rakic.

[1] Ivan Dimitrijevic, Branko Dragovich, Jelena Grujic, Zoran Rakic, A New Model of Nonlocal Modified Gravity, Publications de l'Institut Mathematique (Nouvelle serie) \textbf{94} (108), 187-196 (2013)
[2] Ivan Dimitrijevic, Branko Dragovich, Jelena Grujic, Zoran Rakic, Some Cosmological Solutions of a Nonlocal Modified Gravity, Filomat \textbf{29:3}, 619-628 (2015)