Tracking Quintessence
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910318322515968 |
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| author | Alho, Artur Uggla, Claes Wainwright, John |
| author_facet | Alho, Artur Uggla, Claes Wainwright, John |
| contents | Tracking quintessence, in a spatially flat and isotropic space-time with a minimally coupled canonical scalar field and an asymptotically inverse power-law potential $V(φ)\proptoφ^{-p}$, $p>0$, as $φ\rightarrow0$, is investigated. This is done by introducing a new three-dimensional \emph{regular} dynamical system, which enables a rigorous explanation of the tracking feature: 1) The dynamical system has a tracker fixed point $\mathrm{T}$ with a two-dimensional stable manifold that pushes an open set of nearby solutions toward a single tracker solution originating from $\mathrm{T}$. 2) All solutions, including the tracker solution and the solutions that track/shadow it, end at a common future attractor fixed point that depends on the potential. Thus, the open set of solutions that shadow the tracker solution share its properties during the tracking quintessence epoch. We also discuss similarities and differences of underlying mechanisms for tracking, thawing and scaling freezing quintessence, and, moreover, we illustrate with state space pictures that all of these types of quintessence exist simultaneously for certain potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16775 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tracking Quintessence Alho, Artur Uggla, Claes Wainwright, John General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics Mathematical Physics Dynamical Systems Tracking quintessence, in a spatially flat and isotropic space-time with a minimally coupled canonical scalar field and an asymptotically inverse power-law potential $V(φ)\proptoφ^{-p}$, $p>0$, as $φ\rightarrow0$, is investigated. This is done by introducing a new three-dimensional \emph{regular} dynamical system, which enables a rigorous explanation of the tracking feature: 1) The dynamical system has a tracker fixed point $\mathrm{T}$ with a two-dimensional stable manifold that pushes an open set of nearby solutions toward a single tracker solution originating from $\mathrm{T}$. 2) All solutions, including the tracker solution and the solutions that track/shadow it, end at a common future attractor fixed point that depends on the potential. Thus, the open set of solutions that shadow the tracker solution share its properties during the tracking quintessence epoch. We also discuss similarities and differences of underlying mechanisms for tracking, thawing and scaling freezing quintessence, and, moreover, we illustrate with state space pictures that all of these types of quintessence exist simultaneously for certain potentials. |
| title | Tracking Quintessence |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2311.16775 |