Brane cosmology with a bulk scalar field

We consider ``cosmologically symmetric'' (i.e., solutions with homogeneity and isotropy along three spatial dimensions) five-dimensional spacetimes with a scalar field and a three-brane representing our universe. We write Einstein's equations in a conformal gauge, using light-cone coordinates. We obtain explicit solutions: (a) assuming proportionality between the scalar field and the logarithm of the (bulk) scale factor; (b) assuming separable solutions. We then discuss the cosmology in the brane induced by these solutions.