  We consider the Abelian Higgs model in the broken phase as a spectator in
cosmological spaces of general $D$ space-time dimensions, and allow for the
condensate to be time-dependent. We fix the unitary gauge using Dirac's
formalism for constrained systems, and then quantize the gauge-fixed system.
Vector and scalar perturbations develop time-dependent masses. We work out
their propagators assuming the cosmological background is that of power-law
inflation, characterized by a constant principal slow-roll parameter, and that
the scalar condensate is in the attractor regime, scaling as the Hubble rate.
Our propagators correctly reduce to known results in the Minkowski and de
Sitter space limits. We use the vector propagator to compute the equal-time
correlators of electric and magnetic fields and find that at super-Hubble
separations the former is enhanced, while the latter is suppressed compared to
the vacuum fluctuations of the massless vector field. These correlators satisfy
the hierarchy governed by Faraday's law.
