Gradient expansion formalism for magnetogenesis in the kinetic coupling model

TL;DR

This paper develops a gradient expansion formalism to model magnetogenesis during inflation in the kinetic coupling model, effectively capturing the evolution of electromagnetic fields and energy densities with high accuracy.

Contribution

It introduces a novel set of functions and an infinite chain of equations to describe superhorizon mode amplification, enabling accurate modeling with few equations.

Findings

Accurately describes electric and magnetic energy densities during inflation.

Effective truncation of the equation chain achieves high accuracy.

Applicable to various coupling functions and regimes.

Abstract

In order to describe magnetogenesis during inflation in the kinetic coupling model, we utilize a gradient expansion which is based on the fact that only long-wavelength (superhorizon) modes undergo amplification. For this purpose, we introduce a set of functions (bilinear combinations of electromagnetic fields with an arbitrary number of spatial curls) satisfying an infinite chain of equations. Apart from the usual mode enhancement due to interaction with the inflaton, these equations also take into account the fact that the number of relevant modes constantly grows during inflation. Truncating this chain, we show that even with a relatively small number of equations, it is possible to describe the electric and magnetic energy densities with a few percent accuracy during the whole inflation stage. We arrive at this conclusion for different types of coupling functions (increasing, decreasing, and nonmonotonic) in the regime with strong backreaction and its absence.