Can slow roll inflation induce relevant helical magnetic fields?

Abstract

We study the generation of helical magnetic fields during single fieldinflation induced by an axial coupling of the electromagnetic field tothe inflaton. During slow roll inflation, we find that such a couplingalways leads to a blue spectrum with B2(k)∝k, as long as thetheory is treated perturbatively. The magnetic energy density at the endof inflation is found to be typically too small to backreact on the backgrounddynamics of the inflaton. We also show that a short deviation from slowroll does not result in strong modifications to the shape of the spectrum.We calculate the evolution of the correlation length and the fieldamplitude during the inverse cascade and viscous damping of the helicalmagnetic field in the radiation era after inflation. We conclude thatexcept for low scale inflation with very strong coupling, themagnetic fields generated by such an axial coupling in single field slowroll inflation with perturbative coupling to the inflaton are too weak to provide the seeds for the observed fields in galaxies andclusters.