Inflationary magnetogenesis of primordial magnetic fields with multiple vector fields

TL;DR

This paper explores how multiple vector fields during inflation can generate scale-invariant primordial magnetic fields, introducing a coupling matrix and analyzing different interaction scenarios to address the strong coupling problem.

Contribution

It introduces a coupling matrix for multiple vector fields during inflation and analyzes their effects on magnetogenesis, including cases with no mutual-coupling and with mutual-coupling.

Findings

Scale-invariant magnetic spectra can be achieved without strong coupling issues.

Weak mutual-coupling results in a slightly blue magnetic spectrum.

Strong mutual-coupling can produce scale-invariant spectra but risks backreaction or dilution.

Abstract

In this paper, we discussed the multiple vector fields during the inflation era and the inflationary magnetogenesis with multiple vector fields. Instead of a single coupling function in single vector field models, the coupling matrix between vector fields and scalar field which drive the inflation is introduced. The dynamical equations for multiple vector fields are obtained and applied to the inflation era. We discussed three cases for the double-field model. In no mutual-coupling case, one can find that both electric and magnetic spectrum can be scale-invariant at the end of inflation, meanwhile, the strong coupling problem can be avoided. The effect of mutual-coupling between different vector fields is also discussed. We found that weak mutual-coupling can lead to the slightly blue spectrum of the magnetic field. On the other hand, in the strong mutual-coupling case, the scale-invariant magnetic spectrum can also be obtained but the energy density of electromagnetic fields either lead to the backreaction problem or is diluted by inflation.