The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant

TL;DR

This paper proves the global stability of certain cosmological solutions to the Euler-Einstein system with a positive cosmological constant, showing that small irrotational perturbations do not disrupt the accelerated expansion.

Contribution

It establishes the future stability and geodesic completeness of Friedmann-Lemaître-Robertson-Walker solutions under small irrotational perturbations in the Euler-Einstein system with a positive cosmological constant.

Findings

Background solutions are globally future asymptotically stable.

Perturbed spacetimes are future causally geodesically complete.

Stability holds for a range of sound speeds c_s^2 between 0 and 1/3.

Abstract

In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the Euler-Einstein system with a positive cosmological constant in 1 + 3 dimensions. The background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. We show that under the equation of state p = c_s^2*(energy density), 0 < c_s^2 < 1/3, the background solutions are globally future asymptotically stable under small irrotational perturbations. In particular, we prove that the perturbed spacetimes, which have the topological structure [0,infinity) x T^3, are future causally geodesically complete.