The Einstein-Vlasov System with a Scalar Field

Abstract

We study the Einstein-Vlasov system coupled to a nonlinear scalar field with a nonnegative potential in locally spatially homogeneous space-time, 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 space-time towards the future. The asymptotic behavior of solutions of this system in the future time is analyzed in various aspects, which shows power-law expansion.

The Einstein-Vlasov System/Kinetic Theory

“…Lee considers in [107] the case where a non-linear scalar field is coupled to Vlasov matter. The form of the energy momentum tensor then reads Here ϕ is the scalar field and V is a potential, and the Bianchi identities lead to the following equation for the scalar field: Under the assumption that V is a non-negative C 2 function, global existence to the future is obtained, and if the potential is restricted to the form where , then future geodesic completeness is proven.…”

Global existence of solutions to the Einstein–Maxwell–Massive scalar field system in 3 + 1 formulation on Bianchi spacetimes

“…More details on this question can be found in [5], [21]. In fact, several authors realized the interest of coupling scalar field to other fields equations; see for instance [4], [18], [20], [24], [8].…”

Power-Law Inflation in Spacetimes Without Symmetry

“…A similar discussion for a potential with a strictly positive lower bound is given in [2]. For wider classes of potentials the only mathematical theorems concern spatially homogeneous spacetimes of Bianchi types I-VIII, including normal matter [8,10,13].…”