Beijing Journal of Pure and Applied Mathematics

Volume 1 (2024)

Number 2

Past stability of FLRW solutions to the Einstein-Euler-scalar field equations and their big bang singularities

Pages: 515 – 637

DOI: https://dx.doi.org/10.4310/BPAM.2024.v1.n2.a4

Authors

Florian Beyer (Dept. of Mathematics and Statistics, University of Otago, Dunedin, New Zealand)

Todd A. Oliynyk (School of Mathematical Sciences, Monash University, Melbourne, Victoria, Australia)

Abstract

We establish, in spacetime dimensions $n \geq 3$, the nonlinear stability in the contracting direction of Friedmann-Lemaître-Robertson-Walker (FLRW) solutions to the Einstein-Euler-scalar field equationswith linear equations of state $P={c_{s}^{2}}\rho$ for sounds speeds $c_s$ satisfying $1/(n-1) < c_s^2 < 1$. We further show that nonlinear perturbations of the FLRW solutions are asymptotically pointwise Kasner and terminate in crushing, asymptotically velocity term dominated (AVTD) big bang singularities characterised by curvature blow-up.

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This work is dedicated to the memory of Robert Bartnik.

Received 14 August 2023

Accepted 28 February 2024

Published 17 July 2024