Non-conventional cosmology from a brane universe

We consider brane universes, where energy density is confined ro four-dimensional hypersurfaces (three-branes) whereas one extra compact dimension is felt by gravity only. We show that the cosmology of such branes, when the bulk stress-energy tensor is neglected, is definitely different from standard cosmology and identify the reasons behind this difference. We give a new class of exact solutions with a constant five-dimensional radius and cosmologically evolving brane. We discuss various consequences. (C) 2000 Elsevier Science B.V. All rights reserved.