Non-Gaussian features of primordial magnetic fields in power-law
  inflation
  We show that a conformal-invariance violating coupling of the inflaton to
electromagnetism produces a cross correlation between curvature fluctuations
and a spectrum of primordial magnetic fields. According to this model, in the
case of power-law inflation, a primordial magnetic field is generated with a
nearly flat power spectrum and rms amplitude ranging from nG to pG. We study
the cross correlation, a three-point function of the curvature perturbation and
two powers of the magnetic field, in real and momentum space. The
cross-correlation coefficient, a dimensionless ratio of the three-point
function with the curvature perturbation and magnetic field power spectra, can
be several orders of magnitude larger than expected as based on the amplitude
of scalar metric perturbations from inflation. In momentum space, the
cross-correlation peaks for flattened triangle configurations, and is three
orders of magnitude larger than the squeezed triangle configuration. These
results suggest likely methods for distinguishing the observational signatures
of the model.
