When tadpoles matter: One-loop corrections for spectator Higgs in inflation

We consider the classical attractor regime of the spectator Abelian Higgs model in power-law inflation, and compute the one-loop corrections to its evolution. For computations we utilize dimensional regularization and the propagators in the unitary gauge. The corrections to both the scalar condensate and the energy-momentum tensor exhibit secular ultraviolet contributions, that tend to slow down the rolling of the scalar down its potential, and drive it away from the classical attractor. These corrections need not be suppressed if the U(1) charge is much larger than the scalar self-coupling, which is seen already in flat space. In addition, at late times the secular corrections necessarily invalidate the perturbative loop expansion. We find the late time secular corrections to be captured by the renormalization group, which opens up the possibility to resum them past the breakdown of perturbativity.