Nonlocal de Sitter Gravity and Cosmology

Despite its great success, the general theory of relativity is not the final theory of gravity. In addition to other problems, some shortcomings of the standard model of cosmology led to the search for a more general theory of gravity. One of the promising lines of research is the nonlocal theory of gravity. In this talk, I will present a simple nonlocal de Sitter gravity and its several exact vacuum cosmological solutions. One of these solutions mimics effects that are usually assigned to dark matter and dark energy. Some other solutions are examples of the bounce and cyclic universes. The application of this nonlocal gravity model to describe the rotation curves of spiral galaxies, as well as some other its aspects, will be also presented.
This talk is mainly based on the paper published in JHEP 12 (2022) 054.