Electric-magnetic duality and the conditions of inflationary magnetogenesis

The magnetogenesis scenarios triggered by the early variation of the gauge coupling are critically analyzed. In the absence of sources, it is shown that the electric power spectra can be explicitly computed from the magnetic power spectra by means of electric-magnetic duality transformations. In the absence of sources the reverse is also true. The remnants of a pre-inflationary expansion and the reheating process break explicitly electric-magnetic duality by inducing Ohmic currents. The generation of large-scale magnetic field and the physical distinction between electric and magnetic observables stems, in this class of models, from the final value reached by the conductivity of the plasma right after inflation. Specific numerical examples are given. The physical requirements of viable magnetogenesis scenarios are spelled out