  In this work we investigate the asymptotic behaviour of solutions to the
Einstein equations with a minimally coupled scalar field. The primary focus of
the present paper here establishing under what conditions a solution becomes
"asymptotically Kasner" sufficiently close to the initial singularity. To
address this question we restrict our attention to Bianchi I space-times. By
restricting our attention to a strictly monotonic scalar field we are able to
provide necessary conditions on a potential so that the resulting solution is
asymptotically Kasner. Moreover, we provide both explicit and numerical
examples of asymptotically Kasner space-times.
