Helical magnetic fields from Riemann coupling

Abstract

We study the inflationary generation of helical magnetic fields from the Riemann coupling with the electromagnetic field. Most models in the literature introduce non-minimal coupling to the electromagnetic fields with a scalar field, hence, breaking the conformal invariance. In this work, we show that non-minimal coupling to the Riemann tensor generates sufficient primordial helical magnetic fields at all observable scales. We explicitly show that one of the helical states decay while the other helical mode increases, leading to a net non-zero helicity. Our model has three key features:~(i) the helical power-spectrum has a slight red-tilt for slow-roll inflation consistent with bounds from observations and free from backreaction problem, (ii) the energy density of the helical fields generated is at least one order of magnitude larger than the scalar-field coupled models, and (iii) unlike the scalar field coupled models, the generated helical fields are insensitive to the reheating dynamics. We show that our model generates the magnetic field of strength 0.01 PicoGauss over Mpc scale.