Some Cosmological Solutions of a New Nonlocal Gravity Model

Abstract

In this paper, we investigate a nonlocal modification of general relativity (GR) with action $S=\frac{1}{16\pi G}\int [R-2\Lambda +(R-4\Lambda )\mathcal{F}(\square )(R-4\Lambda )]\sqrt{-g}{d}^{4}x,$ where $\mathcal{F}(\square )={\sum }_{n=1}^{+\infty }{f}_n{\square }^n$ 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 $\Lambda \ne 0,k=0,$ 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 $\mathcal{F}(\square )$, which satisfies obtained necessary conditions.

13 pages

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