Some Cosmological Solutions of a New Nonlocal Gravity Model

Ivan Dimitrijevic,Branko Dragovich,Zoran Rakic,Alexey S Koshelev,Jelena Stankovic

doi:10.3390/sym12060917

Ivan Dimitrijevic, Branko Dragovich + Show 3 more

Open Access

https://doi.org/10.3390/sym12060917

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Journal: Symmetry	Publication Date: Jun 2, 2020
Citations: 10	License type: CC BY 4.0

Affiliation: University of Belgrade, University of Beira Interior

Abstract

In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1 16 π G ∫ [ R − 2 Λ + ( R − 4 Λ ) F ( □ ) ( R − 4 Λ ) ] − g d 4 x , where F ( □ ) = ∑ n = 1 + ∞ 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 ≠ 0 , k = 0 , and they have no analogs in Einstein’s gravity with cosmological constant Λ . One of these two solutions is a ( t ) = A t e 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.

Highlights

General relativity [1], or in other words Einstein theory of gravity, is recognized as one of the best physical theories—with beautiful theoretical properties and significant phenomenological achievements
From the standard cosmological model, which assumes applicability of General relativity (GR) to the universe as a whole, follows that the universe is approximately made of 68% of dark energy (DE), 27% of dark matter (DM), and only 5% of visible matter
Nonlocal gravity model which we investigate in this paper has P( R) = Q( R) = R − 4Λ, and the action is given explicitly below in Equation (3)

Summary

Introduction

General relativity [1], or in other words Einstein theory of gravity, is recognized as one of the best physical theories—with beautiful theoretical properties and significant phenomenological achievements. To find appropriate solution of equations of motion, the ansatz 2R = rR + s was used, where r and s are parameters that connect the solution and function F (2) If in this case cosmological constant Λ = 0 it is some kind of nonlocal generalization of the Starobinsky R2 inflation model, whose various properties are studied in [19,20]. Another very intriguing example of the nonlocal gravity in Equation (2) has P( R) = Q( R) =.

New Nonlocal Gravity Model

Equations of Motion

Ghost-Free Condition

Cosmological Solutions