There are indications of a lower bound on magnetic fields
in the intergalactic media. Since magnetic fields on such large scales are
difficult to generate in the late universe, this might point to inflationary
magnetogenesis as the origin of intergalactic magnetic fields. If the magnetic
fields are generated during inflation, they are naturally correlated with the
inflaton perturbations in a general class of models. This leads to a
consistency relation between the power spectrum of primordial magnetic fields
and the non-Gaussian three-point cross-correlation of magnetic fields with the
inflaton perturbation. The size of non-Gaussianity can be expressed in a new
magnetic non-linearity parameter b_NL. In the flattened shape where the
non-Gaussianity is maximal, b_NL can be as large as 5000.
