Time reparameterization in Bianchi type I spinor cosmology

TL;DR

This paper explores how to handle time reparameterization in a Bianchi-I universe with a massive Dirac spinor, identifying intrinsic and extrinsic times and solving the quantum Hamiltonian constraint.

Contribution

It introduces a novel approach to time reparameterization in spinor cosmology by using scale factors and spinor scalar character as intrinsic and extrinsic times, respectively.

Findings

Derived exact solutions for the quantum Hamiltonian with chosen time parameters.

Established a consistent method for classical and quantum time reparameterization in Bianchi-I models.

Presented a framework for solving the Hamiltonian constraint after time identification.

Abstract

The problem of time reparameterization is addressed at both the classical and quantum levels in a Bianchi-I universe in which the matter source is a massive Dirac spinor field. We take the scale factors of the metric as the intrinsic time and their conjugate momenta as the extrinsic time. A scalar character of the spinor field is identified as a representation of the extrinsic time. The construction of the field equations and quantization of the model is achieved by solving the Hamiltonian constraint after time identification has been dealt with. This procedure leads to a true Hamiltonian whose exact solutions for the above choices of time are presented