RECORD
The Stability of Relativistic Fluids in Linearly Expanding Cosmologies
Analysis of PDEs · Submitted 26 Jan 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In total, this is indicative that structure formation in cosmological fluid-filled spacetimes requires an epoch of decelerated expansion.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
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 $p=K \rho$ 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 $p=K \rho$, $K \in (0,1/3)$. 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we study cosmological solutions to the Einstein--Euler equations. | contribution 0.62 | 0.84 | 0.02 | asserted 0.69 |
| s1 | 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 $p=K \rho$ for the parameter values $K \in (0,1/3)$. | result 0.83 | 0.96 | 0.41 | asserted 1.00 |
| s2 | 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. | contribution 0.50 | 0.86 | 0.07 | asserted 1.00 |
| s3 | 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 $p=K \rho$, $K \in (0,1/3)$. | result 0.80 | 0.97 | 0.24 | asserted 1.00 |
| s4 | Our proof requires a correction mechanism to account for the spatially curved geometry. | method 0.94 | 0.86 | 0.04 | asserted 1.00 |
| s5 | In total, this is indicative that structure formation in cosmological fluid-filled spacetimes requires an epoch of decelerated expansion. | interpretation 1.00 | 0.44 | 0.44 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original 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 $p=K \rho$ 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 $p=K \rho$, $K \in (0,1/3)$. 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.
Human review
How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 3 sentences without a confident label
Cites as background 2 papers
-
In the context of Einstein-Euler, stability of homogeneous solutions on exponentially expanding cosmological spacetimes was first studied in [ref] , with several later works [ref] .
On the stability of relativistic perfect fluids with linear equations of state $p=K\rho$ where $1/3<K<1$ · Fluid stabilisation from cosmological expansion · 0.92
-
For various other results on fluid stabilization in the regime of accelerated expansionpurple, we refer to [ref] .
The nonlinear stability of n+1 dimensional FLRW spacetimes · Fluid stabilisation from cosmological expansion · 0.81
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.