On the stability of thick brane worlds non-minimally coupled to gravity

TL;DR

This paper investigates the stability of thick brane models in five dimensions where a scalar field non-minimally couples to gravity, showing that such configurations are generally stable with a continuous spectrum of gravitational and scalar modes.

Contribution

It demonstrates the perturbative stability of non-minimally coupled thick branes and analyzes their spectrum using supersymmetric quantum mechanics techniques.

Findings

Stability is generally guaranteed for these branes.

The spectrum includes a continuous tower of spin 2 and spin 0 states.

A non-normalizable zero-mass scalar state is present in regular geometries.

Abstract

We analyze a class of 5D models where a 3 brane is generated by a bulk scalar field non minimally coupled to gravity. We show that perturbative stability of such branes is normally guaranteed although non minimal couplings are not innocuous in general. After the physical states are identified the linearized equations for propagating modes are evaluated into a Schroedinger form and supersymmetric quantum mechanics provides the absence of tachyons. The spectrum contains a tower of spin 2 and spin 0 fields with continuous masses starting from zero ones. For regular geometries the scalar spectrum contains a state with zero mass which is always non normalizable. The propagating massive scalar states are repelled off the brane due to a centrifugal potential.