5-DIMENSIONAL COSMOLOGICAL MODELS IN INDUCED MATTER THEORY

A class of five-dimensional space-times that contain four-dimensional hypersurfaces whose intrinsic metrics are Friedman-Robertson-Walker (FRW) metrics is examined (the four-dimensional intrinsic Lorentzian metrics are both spatially homogeneous and isotropic). The five-dimensional vacuum field equations, (5)G(ij)=O, are shown to induce four-dimensional perfect-fluid FRW held equations, (4)G(ij)=T-4(ij), and thus these FRW cosmological models may be interpreted as being purely geometrical in origin.