On the non-Gaussian correlation of the primordial curvature perturbation
  with vector fields
  We compute the three-point cross-correlation function of the primordial
curvature perturbation generated during inflation with two powers of a vector
field in a model where conformal invariance is broken by a direct coupling of
the vector field with the inflaton. If the vector field is identified with the
electromagnetic field, this correlation would be a non-Gaussian signature of
primordial magnetic fields generated during inflation. We find that the signal
is maximized for the flattened configuration where the wave number of the
curvature perturbation is twice that of the vector field and in this limit, the
magnetic non-linear parameter becomes as large as |b_{NL}| ~ 10^3. In the
squeezed limit where the wave number of the curvature perturbation vanishes,
our results agree with the magnetic consistency relation derived in
arXiv:1207.4187.
