Non-conventional cosmology from a brane universe

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