Asymptotic behaviour of the Einstein-Vlasov system with a positive cosmological constant

TL;DR

This paper investigates the long-term behavior of solutions to the Einstein-Vlasov system with a positive cosmological constant, establishing their global existence, geodesic completeness, and asymptotic properties in a homogeneous setting.

Contribution

It provides new results on the global existence, geodesic completeness, and asymptotic analysis of solutions for the Einstein-Vlasov system with positive cosmological constant in homogeneous spacetimes.

Findings

Solutions exist globally in time.

Solutions are geodesically complete.

Asymptotic behavior of solutions is characterized.

Abstract

We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic behaviour of solutions in the future time is investigated in various aspects.