  Higgs inflation uses the gauge variant Higgs field as the inflaton. During
inflation the Higgs field is displaced from its minimum, which results in
associated Goldstone bosons that are apparently massive. Working in a minimally
coupled U(1) toy model, we use the closed-time-path formalism to show that
these Goldstone bosons do contribute to the one-loop effective action.
Therefore the computation in unitary gauge gives incorrect results. Our
expression for the effective action is gauge invariant upon using the
background equations of motion.
