Effective action for the Abelian Higgs model in FLRW

TL;DR

This paper calculates the divergent quantum corrections to the Abelian Higgs model in an expanding universe, accounting for a time-dependent scalar field, and demonstrates gauge invariance of the results.

Contribution

It provides a detailed one-loop effective action calculation for the Abelian Higgs model in FLRW spacetime with a dynamic scalar field, ensuring gauge invariance.

Findings

Divergent contributions to the one-loop action are explicitly computed.

The calculation confirms gauge invariance when using equations of motion.

The method accommodates a time-dependent scalar expectation value in curved spacetime.

Abstract

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.