Future $T^2$ symmetry Einstein-Vlasov-Scalar field system

TL;DR

This paper establishes local existence of solutions for a cosmological Einstein-Vlasov-scalar field system with $T^2$ symmetry, using short-time PDE existence theorems in areal coordinates.

Contribution

It provides the first proof of local existence for the Einstein-Vlasov-scalar field system with $T^2$ symmetry in an expanding universe.

Findings

Proves local existence of solutions in expanding $T^2$ symmetric models.

Uses PDE short-time existence theorems in areal coordinates.

Models include distribution functions and scalar fields as sources.

Abstract

We prove local existence of solutions in the case of cosmological models for the Einstein-Vlasov-scalar field system with $T^2$ symmetry in expanding direction. This proof is based on short-time existence theorems for the partial differential equations resulting from the Einstein-Vlasov-Scalar Field system in areal coordinates. The sources of equations are generated by a distribution function and a scalar field, subject to Vlasov and a nonlinear wave equations respectively.