Brane models with a Ricci-coupled scalar field

We consider the problem of a scalar field, non-minimally coupled to gravitythrough a $-\xi\phi^{2}R$ term, in the presence of a Brane. Exact solutions,for a wide range of values of the coupling parameter $\xi$, for both$\phi$-dependent and $\phi$-independent Brane tension, are derived and theirbehaviour is studied. In the case of a Randall-Sundrum geometry, a class of theresulting scalar field solutions exhibits a folded-kink profile. We go beyondthe Randall-Sundrum geometry studying general warp factor solutions in thepresence of a kink scalar. Analytic and numerical results are provided for thecase of a Brane or for smooth geometries, where the scalar field acts as athick Brane. It is shown that finite geometries with warp factors thatasymptotically decrease exponentially are realizable for a wide range ofparameter values. We also study graviton localization in our setup and findthat the localizing potential for gravitons with the characteristicvolcano-like profile develops a local maximum located at the origin for highvalues of the coupling $\xi$.Comment: 20 pages, 14 figure