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Primordial magnetic fields of cosmologically interesting field strengths canbe generated from gravitationally coupled electrodynamics during inflation. Asthe cosmological constraints require this to be power law inflation it is notpossible to generate at the same time the curvature perturbation frominflation. Therefore here a completion is considered whereby the large scalemagnetic field is generated during inflation and the primordial curvature modein a subsequent era from a curvaton field. It is found that constraints on themodel to obtain strong magnetic fields and those to suppress the amplitude ofthe curvature perturbation generated during inflation can be simultaneouslysatisfied for magnetic seed fields $B_s\stackrel{>}{\sim}10^{-30}$ G.

Completing magnetic field generation from gravitationally coupled electrodynamics with the curvaton mechanism