Magnetogenesis, variation of gauge couplings and inflation

The interplay among the possible variation of gauge coupling and the inflationary dynamics is investigated in a simplified toy model. Depending upon various parameters (scalar mass, curvature scale at the end of inflation and at the onset of the radiation epoch), the two-point function of the magnetic inhomogeneities grows during the de Sitter stage of expansion and, consequently, large scale magnetic fields are generated. The requirements coming from inflationary magnetogenesis are examined together with the theoretical constraints stemming from the explicit model of the evolution of the gauge coupling.