Isotropic cosmological singularities 3: The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations

TL;DR

This paper establishes the well-posedness of the Cauchy problem for inhomogeneous conformal Einstein-Vlasov equations describing massless collisionless gas cosmologies with isotropic singularities, using data from the limiting particle distribution.

Contribution

It demonstrates the well-posedness of the Cauchy problem for these equations with data at the singularity, advancing understanding of cosmological models with isotropic singularities.

Findings

Cauchy problem is well-posed for the conformal Einstein-Vlasov system.

Data at the singularity can be specified by the limiting particle distribution.

Provides a mathematical framework for inhomogeneous cosmologies with isotropic singularities.

Abstract

We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. It is shown that the Cauchy problem for these equations is well-posed with data consisting of the limiting particle distribution function at the singularity.