Can slow roll inflation induce relevant helical magnetic fields?

TL;DR

This paper investigates the generation of helical magnetic fields during slow roll inflation with axial coupling, concluding that such fields are generally too weak to seed observed cosmic magnetic fields under typical conditions.

Contribution

It provides a detailed analysis of helical magnetic field generation during slow roll inflation with axial coupling, showing the resulting spectrum is blue and typically insufficient for seeding cosmic magnetic fields.

Findings

Magnetic fields have a blue spectrum with B^2(k) proportional to k.

Magnetic energy density is too small to affect inflaton dynamics.

Generated magnetic fields are generally too weak to seed galactic and cluster magnetic fields.

Abstract

We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton. During slow roll inflation, we find that such a coupling always leads to a blue spectrum with $B^2(k) \propto k$, as long as the theory is treated perturbatively. The magnetic energy density at the end of inflation is found to be typically too small to backreact on the background dynamics of the inflaton. We also show that a short deviation from slow roll does not result in strong modifications to the shape of the spectrum. We calculate the evolution of the correlation length and the field amplitude during the inverse cascade and viscous damping of the helical magnetic field in the radiation era after inflation. We conclude that except for low scale inflation with very strong coupling, the magnetic fields generated by such an axial coupling in single field slow roll inflation with perturbative coupling to the inflaton are too weak to provide the seeds for the observed fields in galaxies and clusters.