Gauge-invariant fluctuations of scalar branes

TL;DR

This paper extends the Bardeen formalism to warped geometries, analyzing gauge-invariant scalar fluctuations of branes, classifying modes, and studying their spectra, revealing non-localized scalar and vector zero modes and corrections to Newton's law.

Contribution

It generalizes the gauge-invariant fluctuation formalism to warped geometries and classifies the modes, providing a detailed spectral analysis using supersymmetric quantum mechanics.

Findings

Tensor modes are localized on the brane, affecting Newton's law.

Scalar and vector zero modes are non-normalizable and not localized.

Massive mode spectra are characterized using supersymmetric quantum mechanics.

Abstract

A generalization of the Bardeen formalism to the case of warped geometries is presented. The system determining the gauge-invariant fluctuations of the metric induced by the scalar fluctuations of the brane is reduced to a set of Schr\"odinger-like equations for the Bardeen potentials and for the canonical normal modes of the scalar-tensor action. Scalar, vector and tensor modes of the geometry are classified according to four-dimensional Lorentz transformations. While the tensor modes of the geometry live on the brane determining the corrections to Newton law, the scalar and and vector fluctuations exhibit non normalizable zero modes and are, consequently, not localized on the brane. The spectrum of the massive modes of the fluctuations is analyzed using supersymmetric quantum mechanics.