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

Abstract

We establish, in spacetime dimensions $n\ge 3$, the nonlinear stability in the contracting direction of Friedmann-Lemaître-Robertson-Walker (FLRW) solutions to the Einstein-Euler-scalar field equations with 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.

arXiv admin note: substantial text overlap with arXiv:2112.07730

Cited by in corpus (3)

• Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state $p=K\rho$ with $0\le K<1/3$
• Mixmaster Fluids Near the Big Bang
• Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability