The Stability of Relativistic Fluids in Linearly Expanding Cosmologies
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909265760878592 |
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| author | Fajman, David Ofner, Maximilian Oliynyk, Todd A. Wyatt, Zoe |
| author_facet | Fajman, David Ofner, Maximilian Oliynyk, Todd A. Wyatt, Zoe |
| contents | In this paper we study cosmological solutions to the Einstein--Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly expanding cosmological spacetimes with a linear equation of state $p=K ρ$ for the parameter values $K \in (0,1/3)$. This removes the restriction to irrotational perturbations in earlier work, and relies on a novel transformation of the fluid variables that is well-adapted to Fuchsian methods. We then apply this new transformation to show the global regularity and stability of the Milne spacetime under the coupled Einstein--Euler equations, again with a linear equation of state $p=K ρ$, $K \in (0,1/3)$. Our proof requires a correction mechanism to account for the spatially curved geometry. In total, this is indicative that structure formation in cosmological fluid-filled spacetimes requires an epoch of decelerated expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11191 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Stability of Relativistic Fluids in Linearly Expanding Cosmologies Fajman, David Ofner, Maximilian Oliynyk, Todd A. Wyatt, Zoe Analysis of PDEs General Relativity and Quantum Cosmology 35Q75, 35Q31, 83C05, 83F05 In this paper we study cosmological solutions to the Einstein--Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly expanding cosmological spacetimes with a linear equation of state $p=K ρ$ for the parameter values $K \in (0,1/3)$. This removes the restriction to irrotational perturbations in earlier work, and relies on a novel transformation of the fluid variables that is well-adapted to Fuchsian methods. We then apply this new transformation to show the global regularity and stability of the Milne spacetime under the coupled Einstein--Euler equations, again with a linear equation of state $p=K ρ$, $K \in (0,1/3)$. Our proof requires a correction mechanism to account for the spatially curved geometry. In total, this is indicative that structure formation in cosmological fluid-filled spacetimes requires an epoch of decelerated expansion. |
| title | The Stability of Relativistic Fluids in Linearly Expanding Cosmologies |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology 35Q75, 35Q31, 83C05, 83F05 |
| url | https://arxiv.org/abs/2301.11191 |