On the structural stability of a simple cosmological model in R + αR2 theory of gravity
The theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann–Robertson–Walker metric is employed to formulate the dynamics in both the Jordan frame and the conformally transformed Einstein frame. We show that, in b...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S037026932400755X |
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| _version_ | 1841550704146120704 |
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| author | Orest Hrycyna |
| author_facet | Orest Hrycyna |
| author_sort | Orest Hrycyna |
| collection | DOAJ |
| description | The theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann–Robertson–Walker metric is employed to formulate the dynamics in both the Jordan frame and the conformally transformed Einstein frame. We show that, in both frames, there are stable de Sitter states where the expansion of the Hubble function naturally includes terms corresponding to an effective dark matter component. Using the invariant centre manifold, we demonstrate that, in the Einstein frame, there exists a zero-measure set of initial conditions that lead from an unstable to a stable de Sitter state. Additionally, the initial de Sitter state is associated with a parallelly propagated singularity. We show that the formulations of the theory in the Jordan frame and the Einstein frame are physically nonequivalent. |
| format | Article |
| id | doaj-art-95ec6a6f90ea4c6f8de37ce8b7ee955f |
| institution | Kabale University |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj-art-95ec6a6f90ea4c6f8de37ce8b7ee955f2025-01-10T04:37:37ZengElsevierPhysics Letters B0370-26932025-01-01860139197On the structural stability of a simple cosmological model in R + αR2 theory of gravityOrest Hrycyna0Theoretical Physics Division, National Centre for Nuclear Research, Ludwika Pasteura 7, 02-093 Warszawa, PolandThe theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann–Robertson–Walker metric is employed to formulate the dynamics in both the Jordan frame and the conformally transformed Einstein frame. We show that, in both frames, there are stable de Sitter states where the expansion of the Hubble function naturally includes terms corresponding to an effective dark matter component. Using the invariant centre manifold, we demonstrate that, in the Einstein frame, there exists a zero-measure set of initial conditions that lead from an unstable to a stable de Sitter state. Additionally, the initial de Sitter state is associated with a parallelly propagated singularity. We show that the formulations of the theory in the Jordan frame and the Einstein frame are physically nonequivalent.http://www.sciencedirect.com/science/article/pii/S037026932400755X |
| spellingShingle | Orest Hrycyna On the structural stability of a simple cosmological model in R + αR2 theory of gravity Physics Letters B |
| title | On the structural stability of a simple cosmological model in R + αR2 theory of gravity |
| title_full | On the structural stability of a simple cosmological model in R + αR2 theory of gravity |
| title_fullStr | On the structural stability of a simple cosmological model in R + αR2 theory of gravity |
| title_full_unstemmed | On the structural stability of a simple cosmological model in R + αR2 theory of gravity |
| title_short | On the structural stability of a simple cosmological model in R + αR2 theory of gravity |
| title_sort | on the structural stability of a simple cosmological model in r αr2 theory of gravity |
| url | http://www.sciencedirect.com/science/article/pii/S037026932400755X |
| work_keys_str_mv | AT oresthrycyna onthestructuralstabilityofasimplecosmologicalmodelinrar2theoryofgravity |