Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field
The stability criteria for the dynamical system of a homogeneous and isotropic cosmological model are investigated with the interaction of a scalar field in the presence of a perfect fluid. In this paper, we depict the dynamical system perspective to study qualitatively the scalar field cosmology un...
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Wiley
2020-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/1805350 |
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| author | S. Surendra Singh Chingtham Sonia |
| author_facet | S. Surendra Singh Chingtham Sonia |
| author_sort | S. Surendra Singh |
| collection | DOAJ |
| description | The stability criteria for the dynamical system of a homogeneous and isotropic cosmological model are investigated with the interaction of a scalar field in the presence of a perfect fluid. In this paper, we depict the dynamical system perspective to study qualitatively the scalar field cosmology under two special cases, with and without potential. In the absence of potential, we get a two-dimensional dynamical system, and we study the analytical as well as geometrical behavior. For the dynamical system with potential, we analyze different potential forms: simple exponential potential form (Vϕ=Voe−λϕ), double exponential potential form Vϕ=Voexp−Aexp2αϕ, and inverse power law potential form (Vϕ=Voϕ−α). We generate an autonomous system of ordinary differential equations (ASODE) for each case by introducing new dimensionless variables and obtain respective fixed points. We also analyze the type, nature, and stability of the fixed points and how their behavior reflects towards the cosmological scenarios. Throughout the whole work, the investigation of this model has shown us the deep connection between these theories and cosmic acceleration phenomena. The phase plots of the system at different conditions and different values of γ have been analyzed in detail, and their geometrical interpretations have been studied. The perturbation plots of the dynamical system have been analyzed with emphasis on our analytical findings. We have evaluated the total energy density (Ωϕ) at the fixed points and also found out the suitable range of γ and λ for a stable model. |
| format | Article |
| id | doaj-art-bf61fc53ccf74e389de85735ffc2e8fa |
| institution | DOAJ |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-bf61fc53ccf74e389de85735ffc2e8fa2025-08-20T03:23:08ZengWileyAdvances in High Energy Physics1687-73571687-73652020-01-01202010.1155/2020/18053501805350Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar FieldS. Surendra Singh0Chingtham Sonia1Department of Mathematics, NIT Manipur, Imphal 795004, IndiaDepartment of Mathematics, NIT Manipur, Imphal 795004, IndiaThe stability criteria for the dynamical system of a homogeneous and isotropic cosmological model are investigated with the interaction of a scalar field in the presence of a perfect fluid. In this paper, we depict the dynamical system perspective to study qualitatively the scalar field cosmology under two special cases, with and without potential. In the absence of potential, we get a two-dimensional dynamical system, and we study the analytical as well as geometrical behavior. For the dynamical system with potential, we analyze different potential forms: simple exponential potential form (Vϕ=Voe−λϕ), double exponential potential form Vϕ=Voexp−Aexp2αϕ, and inverse power law potential form (Vϕ=Voϕ−α). We generate an autonomous system of ordinary differential equations (ASODE) for each case by introducing new dimensionless variables and obtain respective fixed points. We also analyze the type, nature, and stability of the fixed points and how their behavior reflects towards the cosmological scenarios. Throughout the whole work, the investigation of this model has shown us the deep connection between these theories and cosmic acceleration phenomena. The phase plots of the system at different conditions and different values of γ have been analyzed in detail, and their geometrical interpretations have been studied. The perturbation plots of the dynamical system have been analyzed with emphasis on our analytical findings. We have evaluated the total energy density (Ωϕ) at the fixed points and also found out the suitable range of γ and λ for a stable model.http://dx.doi.org/10.1155/2020/1805350 |
| spellingShingle | S. Surendra Singh Chingtham Sonia Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field Advances in High Energy Physics |
| title | Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field |
| title_full | Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field |
| title_fullStr | Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field |
| title_full_unstemmed | Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field |
| title_short | Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field |
| title_sort | dynamical system perspective of cosmological models minimally coupled with scalar field |
| url | http://dx.doi.org/10.1155/2020/1805350 |
| work_keys_str_mv | AT ssurendrasingh dynamicalsystemperspectiveofcosmologicalmodelsminimallycoupledwithscalarfield AT chingthamsonia dynamicalsystemperspectiveofcosmologicalmodelsminimallycoupledwithscalarfield |