Inflationary magnetic fields from massive Euler-Heisenberg electrodynamics

We study the generation of cosmic magnetic fields during de Sitter inflation in a non-conformally-invariant effective model of massive electrodynamics containing a four-photon interaction term. We show that, if the photon self-coupling is strong enough, comoving magnetic fields correlated on scales of 10kpc and of intensities 10−22G≲B0≲10−19G are produced as excitation of the vacuum. If amplified by galactic dynamo, they naturally explain the existence of galactic magnetic fields.