  If cosmic magnetic fields are indeed produced during inflation, they are
likely to be correlated with the scalar metric perturbations that are
responsible for the Cosmic Microwave Background anisotropies and Large Scale
Structure. Within an archetypical model of inflationary magnetogenesis, we show
that there exists a new simple consistency relation for the non-Gaussian cross
correlation function of the scalar metric perturbation with two powers of the
magnetic field in the squeezed limit where the momentum of the metric
perturbation vanishes. We emphasize that such a consistency relation turns out
to be extremely useful to test some recent calculations in the literature.
Apart from primordial non-Gaussianity induced by the curvature perturbations,
such a cross correlation might provide a new observational probe of inflation
and can in principle reveal the primordial nature of cosmic magnetic fields.
