Brans–Dicke brane cosmology

A five-dimensional brane cosmology with non-minimally coupled scalar field to gravity is considered in the Jordan frame. We derive the effective four-dimensional field equations on a (3+1)-dimensional brane where the fifth dimension is assumed to have an orbifold symmetry. We show that energy conservation still holds for matter on the brane in spite of the existence of a scalar field (the Brans–Dicke field) in the bulk. Finally, we discuss some cosmological consequences of this setup.