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

Bianchi I "asymptotically Kasner" solutions of the Einstein scalar field equations