Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

TL;DR

This paper proves that under certain symmetries, Einstein-Vlasov models with a positive cosmological constant expand forever, become isotropic, and are geodesically complete, supporting the cosmic no hair conjecture.

Contribution

It demonstrates global existence and asymptotic isotropization for Einstein-Vlasov systems with positive cosmological constant under plane or hyperbolic symmetry.

Findings

Area radius tends to infinity

Spacetimes are future geodesically complete

Expansion becomes exponential and isotropic

Abstract

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes.