# Probabilistic interpretation of the wave function for the Bianchi I model

## TL;DR

This paper compares two quantization approaches for the Bianchi I cosmological model, analyzing their equivalence and interpretative issues, especially regarding the role of isotropic matter in the dynamics.

## Contribution

It provides a detailed comparison of reduced phase space and Vilenkin semiclassical quantization methods for Bianchi I, highlighting conditions for their equivalence.

## Key findings

- The two approaches yield equivalent results when isotropic matter dominates the dynamics.
- Technical and interpretative issues differ between the methods but can be reconciled under certain conditions.
- The role of the isotropic variable as time is crucial for the equivalence of the approaches.

## 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.