Linearized five dimensional Kaluza-Klein theory as a gauge theory

Abstract

We develop a linearized five-dimensional Kaluza-Klein theory as a gauge theory. By perturbing the metric around flat and de Sitter backgrounds, we first discuss linearized gravity as a gauge theory in any dimension. In the particular case of five dimensions, we show that in using the Kaluza-Klein mechanism, the field equations of our approach imply both linearized gauge gravity and Maxwell theory in flat and de Sitter scenarios. As a possible further development of our formalism, we also discuss an application in the context of gravitational polarization scattering by means of the analogue of the Mueller matrix in optical polarization algebra. We argue that this application can be of particular interest in gravitational wave experiments.