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

Jelena Grujić

### Nonlocal Cosmology

Abstract

In this contribution we consider nonlocal gravity action without matter in the form $$S = \int d^{4}x \sqrt{-g}\Big(\frac{R - 2 \Lambda}{16 \pi G} + R^{-1} \mathcal{F}(\Box)R \Big),$$ where $\Box = \frac{1}{\sqrt{-g}} \partial_{\mu}\sqrt{-g} g^{\mu\nu} \partial_{\nu}$, $\mathcal{F}(\Box)= \displaystyle \sum_{n =0}^{\infty} f_{n}\Box^{n}$ is an analytic function of the d'Alembertian $\Box$. We find cosmological solutions for constant scalar curvature for all three values of curvature constant $k = 0,\pm 1$. Among these solutions there are two nonsingular bounce solutions and one singular cyclic cosmic solution, see references [1,2].

[1] I. Dimitrijevic, B.Dragovich, J. Grujic, Z. Rakic, A new model of nonlocal modified gravity'', Publications de l'Institut Mathematique \textbf{94} (108), 187--196 (2013).
[2] Ivan Dimitrijevic, Branko Dragovich, Jelena Grujic, and Zoran Rakic. Constant Curvature Cosmological Solutions in Nonlocal Gravity. In Bunoiu, OM and Avram, N and Popescu, A, editor, TIM 2013 PHYSICS CONFERENCE, volume 1634 of AIP Conference Proceedings, pages 18-23. W Univ Timisoara, Fac Phys, 2014. TIM 2013 Physics Conference, Timisoara, ROMANIA, NOV 21-24, 2013.

This is joint work with I. Dimitrijevic, B. Dragovich and Z. Rakic.