Cosmological solutions of a nonlocal square root gravity

Abstract In this paper we consider modification of general relativity extending R − 2 Λ by nonlocal term of the form R − 2 Λ F ( □ ) R − 2 Λ , where F ( □ ) is an analytic function of the d'Alembert operator □. We have found some exact cosmological solutions of the corresponding equations of motion without matter and with Λ ≠ 0 . One of these solutions is a ( t ) = A t 2 3 e Λ 14 t 2 , which imitates properties similar to an interplay of the dark matter and the dark energy. For this solution we calculated some cosmological parameters which are in a good agreement with observations. This nonlocal gravity model has not the Minkowski space solution. We also found several conditions which function F ( □ ) has to satisfy.