Some Cosmological Solutions of a New Nonlocal Gravity Model

I. Dimitrijevic; B. Dragovich; A. S. Koshelev; Z. Rakic; J. Stankovic

doi:10.3390/sym12060917

paper

Some Cosmological Solutions of a New Nonlocal Gravity Model

arXiv:2006.16041 · doi:10.3390/sym12060917

Abstract

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

arXiv comment13 pages

Some Cosmological Solutions of a New Nonlocal Gravity Model

Abstract

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