Backreaction from gauge fields produced during inflation

TL;DR

This paper investigates the backreaction effects of gauge fields produced during inflation on the background evolution and magnetic field spectrum, extending a formalism to include combined coupling types and applying it to a generalized Starobinsky model.

Contribution

It extends the gradient-expansion formalism to models with both kinetic and axial couplings, enabling self-consistent analysis of backreaction effects during inflation.

Findings

Backreaction significantly alters the gauge field spectrum.

Generated magnetic fields have limited correlation length due to backreaction.

Oscillatory behavior of gauge fields is caused by inflaton response.

Abstract

In this work, we study general features of a regime where gauge fields produced during inflation cause a strong backreaction on the background evolution and its impact on the spectrum and the correlation length of gauge fields. With this aim, the gradient-expansion formalism previously proposed for the description of inflationary magnetogenesis in purely kinetic or purely axial coupling models, is extended to the case when both types of coupling are present. As it is formulated in position space, this method allows us to self-consistently take into account the backreaction of generated gauge fields on the inflationary background because it captures the nonlinear evolution of all physically relevant gauge-field modes at once. Using this extended gradient-expansion formalism, suitable for a wide range of inflationary magnetogenesis models, we study the gauge-field production in a specific generalization of the Starobinsky $R^2$-model with a nonminimal coupling of gauge fields to gravity. In the Einstein frame, this model implies, in addition to an asymptotically flat inflaton potential, also a nontrivial form of kinetic and axial coupling functions which decrease in time and, thus, are potentially suitable for the generation of gauge fields with a scale-invariant or even red-tilted power spectrum. The numerical analysis shows, however, that backreaction, which unavoidably occurs in this model for the interesting range of parameters, strongly alters the behavior of the spectrum and does not allow us to obtain a sufficiently large correlation length for the magnetic field. The oscillatory behavior of the generated field, caused by the retarded response of the gauge field to changes of the inflaton velocity, was revealed.