On nonlocal modified gravity

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 $\Box$. Some of obtained solutions contain effects which are usually assigned to the dark matter and dark energy.