Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations

TL;DR

This paper studies the evolution of Bianchi type I cosmological models with Vlasov matter, revealing that they expand forever and isotropize, with unique past singularities and heteroclinic networks influencing their dynamics.

Contribution

It introduces a detailed dynamical systems analysis of Einstein-Vlasov Bianchi I models, highlighting novel past asymptotic states and heteroclinic structures not seen in perfect fluid models.

Findings

Models expand forever and isotropize over time.

Existence of a heteroclinic network on the past attractor.

Vlasov matter causes different dynamics than perfect fluids.

Abstract

We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the past there exists a singularity. We identify and describe all possible past asymptotic states; in particular, on the past attractor set we establish the existence of a heteroclinic network, which is a new type of feature in general relativity. This illustrates among other things that Vlasov matter can lead to quite different dynamics of cosmological models as compared to perfect fluids.