  The effective approach is applied to the analysis of inflationary
magnetogenesis. Rather than assuming a particular underlying description, all
the generally covariant terms potentially appearing with four space-time
derivatives in the effective action have been included and weighted by
inflaton-dependent couplings. The higher derivatives are suppressed by the
negative powers of a typical mass scale whose specific values ultimately depend
on the tensor to scalar ratio. During a quasi-de Sitter stage the corresponding
corrections always lead to an asymmetry between the hypermagnetic and the
hyperelectric susceptibilities. After presenting a general method for the
estimate of the gauge power spectra, the obtained results are illustrated for
generic models and also in the case of some non-generic scenarios where either
the inflaton has some extra symmetry or the higher-order terms are potentially
dominant.
