Lp. Chimento et al., ISOTROPIC AND ANISOTROPIC N-DIMENSIONAL COSMOLOGIES WITH EXPONENTIAL POTENTIALS, Classical and quantum gravity, 15(1), 1998, pp. 57-74
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.