  We analyse the evolution of primordial magnetic fields in spatially flat
Friedmann universes and reconsider the belief that, after inflation, these
fields decay adiabatically on all scales. Without~abandoning classical
electromagnetism or standard cosmology, we demonstrate that this is not
necessarily the case for superhorizon-sized magnetic fields. The underlying
reason for this is causality, which confines the post-inflationary process of
electric-current formation, electric-field elimination and magnetic-flux
freezing within the horizon. As a result, the adiabatic magnetic decay is not
a~priori guaranteed on super-Hubble scales. Instead, after inflation,
large-scale magnetic fields obey a~power-law solution, where one of the modes
drops at a rate slower than the adiabatic. Whether this slowly decaying mode
can dominate and dictate the post-inflationary magnetic evolution depends on
the initial conditions. These are determined by the evolution of the field
during inflation and by the nature of the transition from the de Sitter phase
to the reheating era and then to the subsequent epochs of radiation and dust.
We discuss two alternative and complementary scenarios to illustrate the role
and the implications of the initial conditions for cosmic magnetogenesis. Our
main claim is that magnetic fields can be superadiabatically amplified after
inflation, as long as they remain outside the horizon. This means that
inflation-produced fields can reach astrophysically relevant residual strengths
without breaking away from standard physics. Moreover, using the same causality
arguments, one can constrain (or in some cases assist) the non-conventional
scenarios of primordial magnetogenesis that amplify their fields during
inflation. Finally, we show that our results extend naturally to the marginally
open and the marginally closed Friedmann universes.
