Cosmological magnetic fields from photon coupling to fermions and bosons in inflation

We consider several gauge invariant higher dimensional operators that couple gravity, gauge fields and scalar or fermionic fields and thus break conformal invariance. In particular, we consider terms that break conformal invariance by the photon coupling to heavy and light fermions. While the coupling to heavy fermions typically do not induce significant magnetic fields, the coupling to light fermions may produce observable magnetic fields when there are a few hundred light fermions. Next we consider Planck scale modifications of the kinetic gauge terms of the form f(phi) F_{mu nu} F^{mu nu} and h(psi) F_{mu nu} \~F^{mu nu}, where f and h are functions of scalar and pseudoscalar fields phi, psi, and F_{mu nu}, ~F^{mu nu} are the gauge field strength and its dual, respectively. For a suitable choice of f sufficiently strong magnetic fields may be produced in inflation to be potentially observable today. The pseudoscalar coupling may lead to birefringence in inflation, but no observable magnetic field amplification. Finally, we show that the photon coupling to metric perturbations produces by far too weak fields to be of cosmological interest.