Cosmological solutions of a nonlocal square root gravity

In this paper we consider modification of general relativity extending R−2Λ by nonlocal term of the form R−2ΛF(□)R−2Λ, 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)=At23eΛ14t2, 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.