Kinetic approach to the Schwinger effect during inflation

TL;DR

This paper investigates how the Schwinger effect influences electric field evolution during inflation using a kinetic approach, revealing oscillatory behavior and non-Markovian currents, with results validated by a hydrodynamic model.

Contribution

It introduces a kinetic framework to analyze the Schwinger effect during inflation, accounting for particle production, thermalization, and non-Markovian currents, advancing understanding of electromagnetic dynamics in early universe models.

Findings

Electric current exhibits non-Markovian behavior.

Electric and magnetic fields oscillate with decreasing amplitude.

Hydrodynamic approach confirms kinetic results.

Abstract

Using the kinetic approach, we study the impact of the charged particles dynamics due to the Schwinger effect on the electric field evolution during inflation. As a simple model of the electric field generation, we consider the kinetic coupling of the electromagnetic field to the inflaton via the term $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ with the Ratra coupling function $f=\exp(\beta\phi/M_{p})$. The production of charged particles is taken into account in the Boltzmann kinetic equation through the Schwinger source term. Produced particles are thermalized due to collisions which we model by using the collision integral in the self-consistent relaxation time approximation. We found that the current of created particles exhibits a non-Markovian character and cannot be described by a simple Ohm's law relation $j\propto E$. On the contrary, the electric current as well as the electric field are oscillatory functions of time with decreasing amplitudes and a phase difference due to the ballistic motion of charged carriers. Our qualitative results are checked by using a hydrodynamic approach. Deriving a closed system of equations for the number, current, and energy densities of charged particles and determining its solution, we find a good agreement with the results obtained in the kinetic approach.