Localized Big Bang Stability of Spacetime Dimensions $n\geq4$

TL;DR

This paper proves the nonlinear stability of certain cosmological solutions in higher-dimensional spacetimes, showing they evolve predictably towards singularities characterized by curvature blow-up, extending previous results to all dimensions $n extgreater=4$.

Contribution

It generalizes the stability analysis of Kasner-scalar field solutions to all spacetime dimensions $n extgreater=4$, demonstrating their asymptotic behavior and singularity formation.

Findings

Perturbed solutions are asymptotically Kasner in higher dimensions.

Solutions are geodesically incomplete in the contracting direction.

Curvature invariants blow up at singularities.

Abstract

We prove the past nonlinear stability of the sub-critical Kasner-scalar field solutions to the Einstein-scalar field equations on a truncated cone domain in spacetime dimensions $n\geq4$. Our analysis demonstrates that the perturbed solutions are asymptotically pointwise Kasner, geodesically incomplete in the contracting direction and terminate at quiescent and crushing singularities characterized by the blow-up of curvature invariants. This work generalizes the result of Beyer-Oliynyk-Zheng in [arXiv:2502.09210v2] to all higher dimensional spacetimes.