Global Dynamics for a relativistic charged and colliding plasma in presence of a massive scalar field on the Robertson-Walker spacetime

TL;DR

This paper establishes the existence of local and global solutions for a coupled Einstein-Maxwell-Boltzmann system with a massive scalar field in a cosmological setting, under specific conditions on initial data and parameters.

Contribution

It introduces a method to prove local and global well-posedness for the Einstein-Maxwell-Boltzmann system with a scalar field in a Robertson-Walker spacetime.

Findings

Derived local-in-time solutions using energy estimates and characteristics.

Proved global-in-time solutions under small initial data and specific cosmological constant conditions.

Established conditions ensuring the uniqueness of solutions.

Abstract

We consider the coupled Einstein-Maxwell-Boltzmann system with cosmological constant in presence of a massive scalar field. The background metric is that of Friedman-Lema\^itre-Robertson-Walker space time in the spatially homogeneous case where the unknown functions only depend on time and not on the space variables $(x^i)$, $i=1,2,3$. By combining the energy estimates method with that of characteristics we derive under suitable conditions on the chock kernel (see Eq. 2.20), a local (in time) solution of the coupled system. Further, under the hypotheses that the data are small in some appropriate norms and that the cosmological constant satisfies $\Lambda > -4\pi m^2\Phi_0^2$, we derive a unique global (in time) solution (Theorem 6.1).