Gauge Invariance, Polar Coordinates and Inflation

TL;DR

This paper addresses gauge dependence in quantum corrections of inflationary models, proposing a practical method using polar-like backgrounds to achieve gauge-invariant predictions, demonstrated in the Abelian Higgs model.

Contribution

It introduces a gauge-invariant approach to inflationary observables via a polar-like background current, simplifying calculations and ensuring gauge independence.

Findings

The proposed shortcut yields gauge-independent inflationary predictions.

Application to the Abelian Higgs model confirms the method's effectiveness.

Gauge-invariant currents lead to gauge-independent effective potentials.

Abstract

We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen's gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.