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

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.