Semiclassical corrections to Kasner cosmologies

We consider the Einstein equations for a Bianchi type I geometry, modified by first-order semiclassical quantum corrections. Using reduction techniques developed by Parker and Simon, we simplify these equations, obtaining reduced forms containing only first and second derivatives. We then find analytical solutions for both the vacuum case and for the case of a perfect fluid with a stiff equation of state. In the vacuum case we find that the Kasner solution maintains the same form in both the classical and semiclassical regimes. In the matter-filled case we observe, however, that a qualitatively different behavior emerges in the semiclassical era. We comment on the nature of these differences.