In this talk we discuss nonlocal de Sitter gravity model. In the Einstein-Hilbert action with $\Lambda$ term, we introduce nonlocality by the following way: $$ S = \frac 1{16\pi G} \int \sqrt{R-2\Lambda}(1+F(\Box))\sqrt{R-2\Lambda} \sqrt{-g} \mathrm d^4 x $$ where $F(\Box) = 1+ \sum_{n=1}^{+\infty} f_n \Box^{n} + \sum_{n=1}^{+\infty} f_{-n} \Box^{-n}$ is an analytic function of the d’Alembert-Beltrami operator $\Box$ and its inverse $\Box^{-1}$. By this way, nonlocal operator $F(\Box)$ is dimensionless. The corresponding equations of motion for the metric $g_{\mu\nu}$ are presented.
We present approximate solutions of the Schwarzschild-de Sitter type metric. The obtained approximate solution is of particular interest for examining the possible role of non-local de Sitter gravity in describing the effects that are usually attributed to dark matter.
This talk is based on joint work with Branko Dragovich, Zoran Rakic and Jelena Stankovic.