New Cosmological Solutions of a Nonlocal Gravity Model

Dimitrijevic, Ivan; Dragovich, Branko; Rakic, Zoran; Stankovic, Jelena

doi:10.48550/arxiv.2112.06312

Cited by 1 publication

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“…This isotropic solution have been found and discussed in papers. 9,10 Moreover there are several more solutions of the flat F LRW model that can be extended to the anisotropic case with constant σ.…”

Section: 2mentioning

confidence: 99%

Nonlocal de Sitter gravity and its exact cosmological solutions

Dimitrijevic

Драгович

Rakic

et al. 2022

J. High Energ. Phys.

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This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with Λ term, we introduce nonlocality by the following way: $$ R-2\Lambda =\sqrt{R-2\Lambda}\kern1em \sqrt{R-2\Lambda}\to \sqrt{R-2\Lambda}\kern1em F\left(\square \right)\kern1em \sqrt{R-2\Lambda} $$ R − 2 Λ = R − 2 Λ R − 2 Λ → R − 2 Λ F □ R − 2 Λ , where $$ F\left(\square \right)=1+{\sum}_{n=1}^{+\infty}\left({f}_n{\square}^n+{f}_{-n}{\square}^{-n}\right) $$ F □ = 1 + ∑ n = 1 + ∞ f n □ n + f − n □ − n is an analytic function of the d’Alembert-Beltrami operator □ and its inverse □−1. By this way, R and Λ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator F(□) is dimensionless. The corresponding equations of motion for gravitational field gμν are presented. The first step in finding some exact cosmological solutions is solving the equation $$ \square \sqrt{R-2\Lambda}=q\sqrt{R-2\Lambda} $$ □ R − 2 Λ = q R − 2 Λ , where q = ζΛ (ζ ∈ R) is an eigenvalue and $$ \sqrt{R-2\Lambda} $$ R − 2 Λ is an eigenfunction of the operator □. We presented and discussed several exact cosmological solutions for homogeneous and isotropic universe. One of these solutions mimics effects that are usually assigned to dark matter and dark energy. Some other solutions are examples of the nonsingular bounce ones in flat, closed and open universe. There are also singular and cyclic solutions. All these cosmological solutions are a result of nonlocality and do not exist in the local de Sitter case.

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Section: 2mentioning

confidence: 99%