Brane models with a Ricci-coupled scalar field

We consider the problem of a scalar field, nonminimally coupled to gravity through a -ξφ²R term, in the presence of a brane. Exact solutions, for a wide range of values of the coupling parameter ξ, for both φ-dependent and φ-independent brane tension, are derived and their behavior is studied. In the case of a Randall-Sundrum geometry, a class of the resulting scalar field solutions exhibits a folded-kink profile. We go beyond the Randall-Sundrum geometry studying general warp factor solutions in the presence of a kink scalar. Analytic and numerical results are provided for the case of a brane or for smooth geometries, where the scalar field acts as a thick brane. It is shown that finite geometries with warp factors that asymptotically decrease exponentially are realizable for a wide range of parameter values. We also study graviton localization in our setup and find that the localizing potential for gravitons with the characteristic volcanolike profile develops a local maximum located at the origin for high values of the coupling ξ.