Isotropic cosmological singularities 2: The Einstein-Vlasov system

TL;DR

This paper studies isotropic singularities in cosmological models governed by the Einstein-Vlasov system, establishing a well-posed initial value problem for spatially-homogeneous cases with specific initial data.

Contribution

It develops the theory of isotropic singularities in the Einstein-Vlasov system and proves the well-posedness of the Cauchy problem for spatially-homogeneous cosmologies.

Findings

Established the general theory of isotropic singularities in Einstein-Vlasov models.

Proved the well-posedness of the Cauchy problem with initial data at the singularity.

Focused on spatially-homogeneous cosmologies with limiting particle distributions.

Abstract

We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy problem for these equations is well-posed with data consisting of the limiting particle distribution function at the singularity.