Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant

TL;DR

This paper presents a new conformal transformation method to prove the future nonlinear stability of FLRW solutions with a positive cosmological constant and linear equation of state, analyzing their asymptotic behavior.

Contribution

The authors develop a novel conformal approach that uniformly handles a range of equation of state parameters to establish stability and asymptotics of perturbed FLRW solutions.

Findings

Proves future nonlinear stability of FLRW solutions with positive cosmological constant.

Provides a uniform method for different equation of state parameters.

Determines the asymptotic behavior of solutions in the far future.

Abstract

We introduce a new method for establishing the future non-linear stability of perturbations of FLRW solutions to the Einstein-Euler equations with a positive cosmological constant and a linear equation of state of the form $p = K \rho$. The method is based on a conformal transformation of the Einstein-Euler equations that compactifies the time domain and can handle the equation of state parameter values $0<K\leq 1/3$ in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.