  We examine the mode functions of the electromagnetic field on spherically
symmetric backgrounds with special attention to the subclass which allows for
the foliation as open Friedmann-Lemaitre (FL) spacetime. It is well-known that
in certain scalar field theories on open FL background there can exist
so-called supercurvature modes, their existence depending on parameters of the
theory. Looking at specific open universe models, such as open inflation and
the Milne universe, we find that no supercurvature modes are present in the
spectrum of the electromagnetic field. This excludes the possibility for
superadiabatic evolution of cosmological magnetic fields within these models
without relying on new physics or breaking the conformal invariance of
electromagnetism.
