ISOTROPIC AND ANISOTROPIC N-DIMENSIONAL COSMOLOGIES WITH EXPONENTIAL POTENTIALS

We investigate (N + 1)-dimensional anisotropic cosmological models wit h a massless scalar held, self-interacting through an exponential pote ntial. The problem is reduced to an FRW model with an additional free, massless scalar field. in the N not equal 1 case we find the exact ge neral solution for the Robertson-Walker spacetime and the N > 3 anisot ropic Bianchi type 1 model which is a product of a Bat (3 + 1)-dimensi onal manifold and an (N - 3)-dimensional torus. In both cases the solu tions present singularities and power-law inflation. In the multidimen sional anisotropic case we also analyse the conditions under which dim ensional reduction can proceed. When N = 1 we consider the gravitation al theory formed by setting the Ricci scalar equal to the trace of the energy-momentum tensor of the matter fields. In this case the exact g eneral solution of the second-order system of gravitational and self-i nteracting scalar field equations exhibit singularities, their most no table departure from the N not equal 1 case being the absence of both particle horizons and power-law inflationary solutions.