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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.15326 |
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| _version_ | 1866909096006909952 |
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| author | Alho, Artur Uggla, Claes |
| author_facet | Alho, Artur Uggla, Claes |
| contents | The equations for quintessential $α$-attractor inflation with a single scalar field, radiation and matter in a spatially flat FLRW spacetime are recast into a regular dynamical system on a compact state space. This enables a complete description of the solution space of these models. The inflationary attractor solution is shown to correspond to the unstable center manifold of a de Sitter fixed point, and we describe connections between slow-roll and dynamical systems approximations for this solution, including Padé approximants. We also introduce a new method for systematically obtaining initial data for quintessence evolution by using dynamical systems properties; in particular, this method exploits that there exists a radiation dominated line of fixed points with an unstable quintessence attractor submanifold, which plays a role that is reminiscent of that of the inflationary attractor solution for inflation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15326 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quintessential $α$-attractor inflation: A dynamical systems analysis Alho, Artur Uggla, Claes General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics The equations for quintessential $α$-attractor inflation with a single scalar field, radiation and matter in a spatially flat FLRW spacetime are recast into a regular dynamical system on a compact state space. This enables a complete description of the solution space of these models. The inflationary attractor solution is shown to correspond to the unstable center manifold of a de Sitter fixed point, and we describe connections between slow-roll and dynamical systems approximations for this solution, including Padé approximants. We also introduce a new method for systematically obtaining initial data for quintessence evolution by using dynamical systems properties; in particular, this method exploits that there exists a radiation dominated line of fixed points with an unstable quintessence attractor submanifold, which plays a role that is reminiscent of that of the inflationary attractor solution for inflation. |
| title | Quintessential $α$-attractor inflation: A dynamical systems analysis |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2306.15326 |