Observables in theories with a varying fine structure constant

TL;DR

This paper demonstrates that two different scalar-coupled electrodynamics theories are mathematically equivalent and produce identical physical observables, as exemplified by their interpretation of Cosmic Microwave Background data.

Contribution

It clarifies the equivalence of two parametrizations of scalar electrodynamics theories and their consistent physical predictions.

Findings

Both theories yield the same physical observables.

Differences lie only in phenomenological interpretation.

Application to Cosmic Microwave Background observations supports the equivalence.

Abstract

We show how two seemingly different theories with a scalar multiplicative coupling to electrodynamics are actually two equivalent parametrisations of the same theory: despite some differences in the interpretation of some phenemenological aspects of the parametrisations, they lead to the same physical observables. This is illustrated on the interpretation of observations of the Cosmic Microwave Background.