On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field

TL;DR

This paper analyzes the Einstein-Vlasov-Fokker-Planck system under cosmological conditions, establishing existence, blow-up behavior, and large-time dynamics of solutions, aligning with cosmological expansion phases.

Contribution

It provides the first rigorous analysis of global and blow-up solutions for the Einstein-Vlasov-Fokker-Planck system with cosmological scalar fields.

Findings

Existence of global solutions under certain initial conditions.

Finite-time blow-up solutions depending on initial data.

Large-time behavior shows phases of decelerated and accelerated expansion.

Abstract

The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global solutions and solutions that blow-up in finite time depending on the size of certain functions of the initial data. We also derive information on the large-time behavior of global solutions and toward the singularity for solutions which blow-up in fine time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology.