Dynamical system analysis in teleparallel gravity with boundary term
Abstract In this paper, we perform the dynamical system analysis of the cosmological models framed in the extended teleparallel gravity, the f(T, B) gravity. We use the mapping, $$f(T, B)\rightarrow -T+\tilde{f}(T, B)$$ f ( T , B ) → - T + f ~ ( T , B ) , and define the dynamical variables to form t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-11937-6 |
| _version_ | 1797647220601782272 |
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| author | S. A. Kadam Ninaad P. Thakkar B. Mishra |
| author_facet | S. A. Kadam Ninaad P. Thakkar B. Mishra |
| author_sort | S. A. Kadam |
| collection | DOAJ |
| description | Abstract In this paper, we perform the dynamical system analysis of the cosmological models framed in the extended teleparallel gravity, the f(T, B) gravity. We use the mapping, $$f(T, B)\rightarrow -T+\tilde{f}(T, B)$$ f ( T , B ) → - T + f ~ ( T , B ) , and define the dynamical variables to form the autonomous dynamical system. The critical points are obtained in two well-motivated forms of f(T, B), one that involves the logarithmic form of the boundary term B, and the other one is the non-linear form of the boundary term. The position of critical points is shown in the different evolutionary phases of the Universe such as radiation, matter, and de-Sitter phase. The stability condition of each of the critical points of both the models is derived and the behavior of each point has been obtained mathematically and through the phase portrait. The evolution of standard density parameters such as radiation ( $$\Omega _{r}$$ Ω r ), matter ( $$\Omega _{m}$$ Ω m ), and dark energy ( $$\Omega _{DE}$$ Ω DE ) are also analyzed. Further to connect with the present cosmological scenario, the behavior of deceleration and equation of state parameter both in the dark energy phase ( $$\omega _{DE}$$ ω DE ) and total ( $$\omega _{tot}$$ ω tot ) are shown from the initial condition of the dynamical variables. The accelerating behaviour has been obtained for both models. |
| first_indexed | 2024-03-11T15:14:09Z |
| format | Article |
| id | doaj.art-c94aca65957a4bb790d884f16e0407d8 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-03-11T15:14:09Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-c94aca65957a4bb790d884f16e0407d82023-10-29T12:33:47ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-09-0183911210.1140/epjc/s10052-023-11937-6Dynamical system analysis in teleparallel gravity with boundary termS. A. Kadam0Ninaad P. Thakkar1B. Mishra2Department of Mathematics, Birla Institute of Technology and Science-PilaniDepartment of Mathematics, Birla Institute of Technology and Science-PilaniDepartment of Mathematics, Birla Institute of Technology and Science-PilaniAbstract In this paper, we perform the dynamical system analysis of the cosmological models framed in the extended teleparallel gravity, the f(T, B) gravity. We use the mapping, $$f(T, B)\rightarrow -T+\tilde{f}(T, B)$$ f ( T , B ) → - T + f ~ ( T , B ) , and define the dynamical variables to form the autonomous dynamical system. The critical points are obtained in two well-motivated forms of f(T, B), one that involves the logarithmic form of the boundary term B, and the other one is the non-linear form of the boundary term. The position of critical points is shown in the different evolutionary phases of the Universe such as radiation, matter, and de-Sitter phase. The stability condition of each of the critical points of both the models is derived and the behavior of each point has been obtained mathematically and through the phase portrait. The evolution of standard density parameters such as radiation ( $$\Omega _{r}$$ Ω r ), matter ( $$\Omega _{m}$$ Ω m ), and dark energy ( $$\Omega _{DE}$$ Ω DE ) are also analyzed. Further to connect with the present cosmological scenario, the behavior of deceleration and equation of state parameter both in the dark energy phase ( $$\omega _{DE}$$ ω DE ) and total ( $$\omega _{tot}$$ ω tot ) are shown from the initial condition of the dynamical variables. The accelerating behaviour has been obtained for both models.https://doi.org/10.1140/epjc/s10052-023-11937-6 |
| spellingShingle | S. A. Kadam Ninaad P. Thakkar B. Mishra Dynamical system analysis in teleparallel gravity with boundary term European Physical Journal C: Particles and Fields |
| title | Dynamical system analysis in teleparallel gravity with boundary term |
| title_full | Dynamical system analysis in teleparallel gravity with boundary term |
| title_fullStr | Dynamical system analysis in teleparallel gravity with boundary term |
| title_full_unstemmed | Dynamical system analysis in teleparallel gravity with boundary term |
| title_short | Dynamical system analysis in teleparallel gravity with boundary term |
| title_sort | dynamical system analysis in teleparallel gravity with boundary term |
| url | https://doi.org/10.1140/epjc/s10052-023-11937-6 |
| work_keys_str_mv | AT sakadam dynamicalsystemanalysisinteleparallelgravitywithboundaryterm AT ninaadpthakkar dynamicalsystemanalysisinteleparallelgravitywithboundaryterm AT bmishra dynamicalsystemanalysisinteleparallelgravitywithboundaryterm |