XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019 VIII School on Geometry and Physics 24-28.06.2019
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# Zoran Rakić

## On Non-Local Modified Gravity

Many significant gravitational phenomena have been discovered and predicted using general theory of relativity. Despite to all of this it is not a complete theory. One of actual approaches towards more complete theory of gravity is its nonlocal modication. We consider nonlocal modication of the Einstein theory of gravity in framework of the pseudo-Riemannian geometry. The nonlocal term has the form $\mathcal H(R)\mathcal F(\square)\mathcal G(R)$, where $\mathcal H$ and $\mathcal G$ are differentiable functions of the scalar curvature $R$, and $F(\square) = \sum_{n=0}^\infty f_n \square^n$ where $f_n$ are analytic functions of the d'Alambert operator $\square$. We are paid our attention to the case where $\mathcal H(R) = \mathcal G(R) = \sqrt{R − 2\Lambda}$. Using calculus of variations we derived the corresponding equations of motion. The variation of action is induced by variation of the metric tensor $g_{\mu\nu}$. We consider several models of the above mentioned type, as well as the case when the scalar curvature is constant. Moreover, we consider space-time perturbations of the de Sitter space. It was shown that gravitational waves are described in the class of nonlocal models $\mathcal H(R)\mathcal F(\square)\mathcal G(R)$, with respect to Minkowski metric by the same equations as in general relativity.

This is joint work with Ivan Dimitrijević, Branko Dragović and Jelena Stanković.

The work was partially supported by the project ON174012 of MPNTR of Republic of Serbia.

 Event sponsored by: University of Bialystok

Webpage by: Tomasz Golinski