Constructing stabilized brane world models in five-dimensional Brans–Dicke theory

We consider brane world models, which can be constructed in the five-dimensional Brans–Dicke theory with bulk scalar field potentials suggested by the supergravity theory. For different choices of the potentials and parameters, we get (i) an unstabilized model with the Randall–Sundrum solution for the metric and constant solution for the scalar field; (ii) models with a flat background and tension-full branes; (iii) stabilized brane world models, one of which reproduces the Randall–Sundrum solution for the metric and gives an exponential solution for the scalar field. We also discuss the relationship between solutions in different frames, with non-minimal and minimal couplings of the scalar field.