The Einstein-Vlasov system with a scalar field

TL;DR

This paper investigates the global existence and asymptotic behavior of solutions to the Einstein-Vlasov system coupled with a nonlinear scalar field in homogeneous cosmological models, highlighting conditions for accelerated expansion and geodesic completeness.

Contribution

It demonstrates the global existence of solutions and analyzes their asymptotic behavior, especially for exponential scalar field potentials, in a cosmological setting.

Findings

Solutions exist globally in time.

Exponential potentials lead to accelerated expansion.

Spacetime is causally geodesically complete.

Abstract

We study the Einstein-Vlasov system coupled to a nonlinear scalar field with a nonnegative potential in locally spatially homogeneous spacetime, as an expanding cosmological model. It is shown that solutions of this system exist globally in time. When the potential of the scalar field is of an exponential form, the cosmological model corresponds to accelerated expansion. The Einstein-Vlasov system coupled to a nonlinear scalar field whose potential is of an exponential form shows the causal geodesic completeness of the spacetime towards the future. The asymptotic behaviour of solutions of this system in the future time is analysed in various aspects, which shows power-law expansion.