Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2508.15303 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915454775197696 |
|---|---|
| author | Bernhardt, Louie |
| author_facet | Bernhardt, Louie |
| contents | We study solutions to the Einstein equations coupled to a nonlinear scalar field with exponential potential. This system admits Friedmann-Lemaître-Robertson-Walker solutions undergoing decelerated expansion, with $\mathbb{T}^3$ spatial topology and scale factor $a(t) = t^p$ for $1/3 < p < 1$. For each $p \in (2/3,1)$, we prove that the corresponding FLRW spacetime is future-stable as a solution to the Einstein-nonlinear scalar field system. Given initial data on a spacelike hypersurface that is sufficiently close to the FLRW data, we show the resulting solution is future-causal geodesically complete, and remains close to the FLRW solution for all time. Moreover, we show the perturbed metric components and scalar field converge to spatially homogeneous functions as $t \rightarrow \infty$. A key feature of our analysis is the decomposition of the metric and scalar field perturbations into their spatial averages and oscillatory remainders with zero average. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion Bernhardt, Louie General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry We study solutions to the Einstein equations coupled to a nonlinear scalar field with exponential potential. This system admits Friedmann-Lemaître-Robertson-Walker solutions undergoing decelerated expansion, with $\mathbb{T}^3$ spatial topology and scale factor $a(t) = t^p$ for $1/3 < p < 1$. For each $p \in (2/3,1)$, we prove that the corresponding FLRW spacetime is future-stable as a solution to the Einstein-nonlinear scalar field system. Given initial data on a spacelike hypersurface that is sufficiently close to the FLRW data, we show the resulting solution is future-causal geodesically complete, and remains close to the FLRW solution for all time. Moreover, we show the perturbed metric components and scalar field converge to spatially homogeneous functions as $t \rightarrow \infty$. A key feature of our analysis is the decomposition of the metric and scalar field perturbations into their spatial averages and oscillatory remainders with zero average. |
| title | Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2508.15303 |