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

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 $0<K\le 1/3$ in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.

Corrected an error in the statement and proof of Theorem B.1. Due to this correction, the statement of the main theorem, Theorem 1.3, differs from the published version in that the 0j components of the metric satisfy slightly weaker decay estimates compared to the published version

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