Cosmological solutions of a nonlocal square root gravity

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 t2}, 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.