  We investigate the possibility to recover a four-dimensional (4D) general
theory of relativity, as embedded in a 5D spacetime where gravity is governed
by a five-dimensional (5D) Brans-Dicke (BD) theory of gravity. Employing the
Gauss-Codazzi-Ricci equations and some ideas of the induced matter theory, we
obtain that when the 5D BD scalar field is only depending of the extra
coordinate, it is possible to recover on every generic 4D hypersurface the
usual Einstein field equations plus a cosmological constant term, with matter
sources described by the energy-momentum tensor of induced matter and where the
cosmological constant under certain conditions can vary with time. Finally to
illustrate the formalism, we give an example in which we induced a cosmological
constant from warped product spaces.

General Relativity and Quantum Cosmology