Some Cosmological Solutions of a New Nonlocal Gravity Model

In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1/16 pi G integral[R - 2 Lambda + (R - 4 Lambda) F(square) (R - 4 Delta)] root-gd(4)x, where F(square) = Sigma(+infinity)(n=1) f(n)square(n) is an analytic function of the d'Alembertian square. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if Lambda not equal 0, k = 0, and they have no analogs in Einstein's gravity with cosmological constant Lambda. One of these two solutions is a(t) = A root t e(Lambda/4t2), 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(t2). For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator F(2), which satisfies obtained necessary conditions.