  The quantum mechanical generation of hypermagnetic and hyperlectric fields in
four-dimensional conformally flat background geometries rests on the
simultaneous continuity of the effective horizon and of the extrinsic curvature
across the inflationary boundary. The junction conditions for the gauge fields
are derived in general terms and corroborated by explicit examples with
particular attention to the limit of a sudden (but nonetheless continuous)
transition of the effective horizon. After reducing the dynamics to a pair of
integral equations related by duality transformations, we compute the power
spectra and deduce a novel class of logarithmic corrections which turn out to
be, however, numerically insignificant and overwhelmed by the conductivity
effects once the gauge modes reenter the effective horizon. In this perspective
the magnetogenesis requirements and the role of the postinflationary
conductivity are clarified and reappraised. As long as the total duration of
the inflationary phase is nearly minimal, quasi-flat hypermagnetic power
spectra are comparatively more common than in the case of vacuum initial data.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology