Exponential-Potential Scalar Field Universes II: The Inhomogeneous Models

We obtain exact solutions for the Einstein equations with an exponential-potential scalar field ($V=\mathrm{\Lambda }{e}^{k\varphi }$) which represent simple inhomogeneous generalizations of Bianchi I cosmologies. Studying these equations numerically we find that in most of the cases there is a certain period of inflationary behaviour for $k^2<2$. We as well find that for $k^2>2$ the solutions homogenize generically at late times. Yet, {\em none of the solutions} isotropize. For some particular values of the integration constants we find a multiple inflationary behaviour for which the deceleration and the inflationary phases interchange each other several times during the history of the model.