Cosmological Solutions of a Nonlocal Square Root Gravity

Abstract

In this paper we consider modification of general relativity extending $R-2\Lambda$ by nonlocal term of the form $\sqrt{R-2\Lambda }\mathcal{F}(\square )\sqrt{R-2\Lambda },$ where $\mathcal{F}(\square )$ is an analytic function of the d'Alembert operator $\square$. We have found some exact cosmological solutions of the corresponding equations of motion without matter and with $\Lambda \ne 0$. One of these solutions is $a(t)=A{t}^{\frac{2}{3}}{e}^{\frac{\Lambda }{14}{t}^2},$ 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 $\mathcal{F}(\square )$ has to satisfy.

version published in Phys. Lett. B