Stability of thick brane worlds nonminimally coupled to gravity

We analyze a class of 5D models where a 3 brane is generated by a bulk scalar field nonminimally coupled to gravity. We show that perturbative stability of such branes is normally guaranteed although nonminimal couplings are not innocuous in general. After the physical states are identified, the linearized equations for the propagating modes are evaluated into a Schroedinger form. 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 massless state which is always non-normalizable. The propagating massive scalar states are repelled off the brane due to a centrifugal potential