Magnetic fields from inflation?

TL;DR

This work assesses whether inflation can generate seeds for cosmic magnetic fields by breaking conformal invariance through either a time-dependent coupling or a non-minimal gravitational coupling. By computing the electromagnetic energy density and enforcing that inflation lasts at least 75 e-folds, the authors derive stringent bounds on the present-day seed field, finding δ_B ≲ 1e-32 G on Mpc scales in most scenarios. A narrowly defined strongly coupled regime (n ≈ 2.2) could yield much larger seeds (∼1e-7 G today), but this regime is not trustworthy due to the initial strong coupling. Overall, inflation alone seems insufficient to explain large-scale magnetic fields, pointing to the need for alternative mechanisms or later amplification by dynamos.

Abstract

We consider the possibility of generation of the seeds of primordial magnetic field on inflation and show that the effect of the back reaction of this field can be very important. Assuming that back reaction does not spoil inflation we find a rather strong restriction on the amplitude of the primordial seeds which could be generated on inflation. Namely, this amplitude recalculated to the present epoch cannot exceed $10^{-32}G$ in $Mpc$ scales. This field seems to be too small to be amplified to the observable values by galactic dynamo mechanism.