On a nonlocal de Sitter gravity

In this paper, we briefly review highlights of nonlocal de Sitter gravity based on the nonlocal term $\sqrt{R-2\mathrm{\Lambda }}\mathcal{F}(\mathrm{\square })\sqrt{R-2\mathrm{\Lambda }}$ in the Einstein-Hilbert action without matter sector. This nonlocal de Sitter gravity model has several exact cosmological FLRW solutions and one of these solutions contains some effects that are usually assigned to dark matter and dark energy. There are also some other interesting and promising properties of this kind of gravity nonlocality. We also review some anisotropic cosmological solutions, and mention the corresponding nonlocal Schwarzschild-de Sitter metric.