On Nonlocal Modified Gravity

Abstract

In the last hundred years many significant gravitational phenomena have been predicted and
discovered by General Relativity (GR), which is still the best theory of gravity. Nevertheless,
due to the great observational discoveries of 20th century some (quantum) theoretical and
(astrophysical and cosmological) phenomenological difficulties of modern gravity have been
motivation to search more general theory of gravity than GR. As a result, many modifications
of GR have been considered. One of promising recent investigations is Nonlocal Modified
Gravity. In this article we present a review of some nonlocal gravity models with their
exact cosmological solutions, in which nonlocality is expressed by an analytic function of the
d’Alembert–Beltrami operator. Some of obtained solutions contain effects which are usually
assigned to the dark matter and dark energy.