Exact Bianchi type I models for an exponential-potential scalar field

A non-local transformation is used to linearize the evolution equation for Bianchi type I universes filled with an exponential-potential scalar field. Among the many new explicit solutions there is a family which shows, for different parameter ranges, the two generic asymptotic behaviours that were previously found in numerical and qualitative analyses. A simpler expression for the general solution allows a better insight into the problem and reveals a damped oscillatory behaviour which corresponds to an effective negative cosmological constant. We are also now able to discuss the existence of initial and final singularities. We found families of explicit singular solutions which represent universes which after evolving from a singularity reach a final anisotropic or isotropic Friedmann - Robertson - Walker stage. There are also solutions which avoid the initial singularity and others with a finite time span.