Effective action for the Abelian Higgs model in FLRW

Abstract

We compute the divergent contributions to the one-loop action of the U(1)\nAbelian Higgs model. The calculation allows for a\nFriedmann-Lemaitre-Robertson-Walker space-time and a time-dependent expectation\nvalue for the scalar field. Treating the time-dependent masses as two-point\ninteractions, we use the in-in formalism to compute the first, second and third\norder graphs that contribute quadratic and logarithmic divergences to the\neffective scalar action. Working in R-xi gauge we show that the result is gauge\ninvariant upon using the equations of motion.\n