Resonant magnetic fields from inflation

We propose a novel scenario to generate primordial magnetic fields during inflation. The mechanism relies on an oscillating coupling of the electromagnetic field to the inflaton, the field that drives the accelerated expansion. This resonant mechanism has two key advantages compared to other scenarios of inflationary magnetogenesis. First of all, it generates a narrow band of magnetic fields at any required wavelength. This means that total energy density is not stored in the smallest scales, a situation that otherwise often leads to issues with strong backreaction on the dynamics of the inflaton. Secondly, our mechanism avoids the need for a strong coupling as the coupling is oscillating rather than growing or decaying exponentially.

Despite these major advantages, we find that the backreaction is still far too large during inflation if the generated magnetic fields are required to explain the observed fields in the intergalactic medium (a strength of order 10^-15 Gauss today on  Megaparsec scales). We provide a more general no-go argument, proving that this problem will apply to any inflationary model in which electromagnetic fluctuations are amplified within the Hubble horizon before their evolution freezes outside the horizon.