Helical magnetic fields from Riemann coupling
  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.
