The Stability of Relativistic Fluids in Linearly Expanding Cosmologies

Author(s)
David Fajman, Maximilian Ofner, Todd A Oliynyk, Zoe Wyatt
Abstract

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 for the parameter values ⁠. This removes the restriction to irrotational perturbations in earlier work [ 15] 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 ⁠, ⁠. 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.

Organisation(s)
Gravitational Physics
External organisation(s)
Monash University, King's College London
Journal
International Mathematics Research Notices
Volume
2024
Pages
4328–4383
No. of pages
56
ISSN
1073-7928
DOI
https://doi.org/10.48550/arXiv.2301.11191
Publication date
10-2023
Peer reviewed
Yes
Austrian Fields of Science 2012
103019 Mathematical physics, 103028 Theory of relativity
Portal url
https://ucrisportal.univie.ac.at/en/publications/the-stability-of-relativistic-fluids-in-linearly-expanding-cosmologies(aa26abb6-8f89-4a2b-960a-2fdfafb05821).html