In this paper, we investigate a nonlocal modification of general relativity (GR) with action $S = \frac{ 1}{ 16\pi G} \int [ R- 2\Lambda + (R-4\Lambda) \, \mathcal{ F}(\Box) \, (R-4\Lambda) ] \, \sqrt{ -g}\; d^4x ,$ where $\mathcal{ F} (\Box) = \sum_{ n=1}^{ +\infty} f_n \Box^n$ is an analytic function of the d'Alembertian $\Box$. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if $\Lambda \neq 0, \, k = 0,$ and they have not analogs in Einsten's gravity with cosmological constant $\Lambda$. One of these two solutions is $ a (t) = A \, \sqrt{ t} \, e^{ \frac{ \Lambda}{ 4} t^2} ,$ that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one -- $ a (t) = A \, e^{ \Lambda t^2}$. For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator $\mathcal{ F}(\Box)$, which satisfies obtained necessary conditions.
Categories: gr-qc hep-th