Enhancing the cross-correlations between magnetic fields and scalar
  perturbations through parity violation
  One often resorts to a non-minimal coupling of the electromagnetic field in
order to generate magnetic fields during inflation. The coupling is expected to
depend on a scalar field, possibly the same as the one driving inflation. At
the level of three-point functions, such a coupling leads to a non-trivial
cross-correlation between the perturbation in the scalar field and the magnetic
field. This cross-correlation has been evaluated analytically earlier for the
case of non-helical electromagnetic fields. In this work, we numerically
compute the cross-correlation for helical magnetic fields. Non-Gaussianities
are often generated as modes leave the Hubble radius. The helical
electromagnetic modes evolve strongly (when compared to the non-helical case)
around Hubble exit and one type of polarization is strongly amplified
immediately after Hubble exit. We find that helicity considerably boosts the
amplitude of the dimensionless non-Gaussianity parameter that characterizes the
amplitude and shape of the cross-correlation between the perturbations in the
scalar field and the magnetic field. We discuss the implications of the
enhancement in the non-Gaussianity parameter due to parity violation.
