Stability of Big Bang singularity for the Einstein-Maxwell-scalar field-Vlasov system in the full strong sub-critical regime

TL;DR

This paper proves the nonlinear stability of Kasner solutions in a complex Einstein-Maxwell-scalar field-Vlasov system, extending previous results to include Vlasov fields and a full strong sub-critical regime.

Contribution

It introduces a new strong sub-critical regime and demonstrates nonlinear stability for the Einstein-Maxwell-scalar field-Vlasov system, expanding prior work on simpler systems.

Findings

Identification of a new strong sub-critical regime.

Proof of nonlinear stability within this regime.

Extension of stability results to a more complex physical system.

Abstract

In $3+1$ dimensions, we study the stability of Kasner solutions for the Einstein-Maxwell-scalar field-Vlasov system. This system incorporates gravity, electromagnetic, weak and strong interactions for the initial stage of our universe. Due to the presence of the Vlasov field, various new challenges arise. By observing detailed mathematical structures and designing new delicate arguments, we identify a new strong sub-critical regime and prove the nonlinear stability with Kasner exponents lying in this full regime. This extends the result of Fournodavlos-Rodnianski-Speck [8] from the Einstein-scalar field system to the physically more complex system with the Vlasov field.