Nonlocal de Sitter gravity and its exact cosmological solutions
Abstract 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 Λ = R − 2 Λ R − 2 Λ → R − 2 Λ F □ R − 2 Λ $$ R-2\Lambda =\sqrt{R-2\Lambda}\kern1em...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2022)054 |
| _version_ | 1797860014476492800 |
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| author | Ivan Dimitrijevic Branko Dragovich Zoran Rakic Jelena Stankovic |
| author_facet | Ivan Dimitrijevic Branko Dragovich Zoran Rakic Jelena Stankovic |
| author_sort | Ivan Dimitrijevic |
| collection | DOAJ |
| description | Abstract This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with Λ term, we introduce nonlocality by the following way: R − 2 Λ = R − 2 Λ R − 2 Λ → R − 2 Λ F □ R − 2 Λ $$ 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} $$ , where F □ = 1 + ∑ n = 1 + ∞ f n □ n + f − n □ − n $$ F\left(\square \right)=1+{\sum}_{n=1}^{+\infty}\left({f}_n{\square}^n+{f}_{-n}{\square}^{-n}\right) $$ is an analytic function of the d’Alembert-Beltrami operator □ and its inverse □ −1. By this way, R and Λ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator F(□) is dimensionless. The corresponding equations of motion for gravitational field g μν are presented. The first step in finding some exact cosmological solutions is solving the equation □ R − 2 Λ = q R − 2 Λ $$ \square \sqrt{R-2\Lambda}=q\sqrt{R-2\Lambda} $$ , where q = ζΛ (ζ ∈ R) is an eigenvalue and R − 2 Λ $$ \sqrt{R-2\Lambda} $$ is an eigenfunction of the operator □. We presented and discussed several exact cosmological solutions for homogeneous and isotropic universe. One of these solutions mimics effects that are usually assigned to dark matter and dark energy. Some other solutions are examples of the nonsingular bounce ones in flat, closed and open universe. There are also singular and cyclic solutions. All these cosmological solutions are a result of nonlocality and do not exist in the local de Sitter case. |
| first_indexed | 2024-04-09T21:39:56Z |
| format | Article |
| id | doaj.art-455567737ec747e28cd9afc0454114b7 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T21:39:56Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-455567737ec747e28cd9afc0454114b72023-03-26T11:05:23ZengSpringerOpenJournal of High Energy Physics1029-84792022-12-0120221212810.1007/JHEP12(2022)054Nonlocal de Sitter gravity and its exact cosmological solutionsIvan Dimitrijevic0Branko Dragovich1Zoran Rakic2Jelena Stankovic3Faculty of Mathematics, University of BelgradeInstitute of Physics, University of BelgradeFaculty of Mathematics, University of BelgradeTeacher Education Faculty, University of BelgradeAbstract This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with Λ term, we introduce nonlocality by the following way: R − 2 Λ = R − 2 Λ R − 2 Λ → R − 2 Λ F □ R − 2 Λ $$ 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} $$ , where F □ = 1 + ∑ n = 1 + ∞ f n □ n + f − n □ − n $$ F\left(\square \right)=1+{\sum}_{n=1}^{+\infty}\left({f}_n{\square}^n+{f}_{-n}{\square}^{-n}\right) $$ is an analytic function of the d’Alembert-Beltrami operator □ and its inverse □ −1. By this way, R and Λ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator F(□) is dimensionless. The corresponding equations of motion for gravitational field g μν are presented. The first step in finding some exact cosmological solutions is solving the equation □ R − 2 Λ = q R − 2 Λ $$ \square \sqrt{R-2\Lambda}=q\sqrt{R-2\Lambda} $$ , where q = ζΛ (ζ ∈ R) is an eigenvalue and R − 2 Λ $$ \sqrt{R-2\Lambda} $$ 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.https://doi.org/10.1007/JHEP12(2022)054Classical Theories of GravityCosmology of Theories BSMModels for Dark Matter |
| spellingShingle | Ivan Dimitrijevic Branko Dragovich Zoran Rakic Jelena Stankovic Nonlocal de Sitter gravity and its exact cosmological solutions Journal of High Energy Physics Classical Theories of Gravity Cosmology of Theories BSM Models for Dark Matter |
| title | Nonlocal de Sitter gravity and its exact cosmological solutions |
| title_full | Nonlocal de Sitter gravity and its exact cosmological solutions |
| title_fullStr | Nonlocal de Sitter gravity and its exact cosmological solutions |
| title_full_unstemmed | Nonlocal de Sitter gravity and its exact cosmological solutions |
| title_short | Nonlocal de Sitter gravity and its exact cosmological solutions |
| title_sort | nonlocal de sitter gravity and its exact cosmological solutions |
| topic | Classical Theories of Gravity Cosmology of Theories BSM Models for Dark Matter |
| url | https://doi.org/10.1007/JHEP12(2022)054 |
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