Cosmological models with one extra dimension

We consider cosmological models in which a homogeneous isotropic universe is embedded as a 3 + 1 dimensional surface into a 4 + 1 dimensional manifold. The size of the extra dimension depends on time. It is small compared to the size of the universe only if the energy of gravitational self-interaction of the universe through the compact extra dimension dominates over all other kinds of energy. The self-interaction energy gives the main contribution into the Friedmann equation, which governs the dynamics of the scale factor of the universe. (C) 2000 Elsevier Science B.V. All rights reserved.