Bianchi type I cosmologies in arbitrary dimensional dilaton gravities

Abstract

We study the low energy string effective action with an exponential type dilaton potential and vanishing torsion in a Bianchi type I space-time geometry. In the Einstein and string frames the general solution of the gravitational field equations can be expressed in an exact parametric form. Depending on the values of the dilaton coupling constant and of the coefficient in the exponential, the obtained cosmological models can be generically divided into three classes, leading to both singular and non-singular behaviors. The effect of the potential on the time evolution of the mean anisotropy parameter is also considered in detail, and it is shown that a Bianchi type I universe isotropizes only in the presence of a dilaton field potential or a central deficit charge.