Probabilistic interpretation of the wave function for the Bianchi I model

Abstract

We compare two different approaches for quantization of the Bianchi I model: a reduced phase space quantization, in which the isotropic Misner variables is taken as time, and the Vilenkin proposal, in which a semiclassical approximation is performed for the same variable. We outline the technical and interpretative issues of these two methods and we demonstrate that they provide equivalent results only if the dynamics is essentially dictated by the isotropic matter contribution.