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

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 $1\mathrm{/}(n-1)<c_s^2<1$. 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.