  We compute the divergent contributions to the one-loop action of the U(1)
Abelian Higgs model. The calculation allows for a
Friedmann-Lemaitre-Robertson-Walker space-time and a time-dependent expectation
value for the scalar field. Treating the time-dependent masses as two-point
interactions, we use the in-in formalism to compute the first, second and third
order graphs that contribute quadratic and logarithmic divergences to the
effective scalar action. Working in R-xi gauge we show that the result is gauge
invariant upon using the equations of motion.
