Separable sequences in Bianchi I loop quantum cosmology

TL;DR

This paper analyzes the properties of sequences arising from solving the Hamiltonian constraint in Bianchi I loop quantum cosmology, revealing time asymmetry around the classical singularity.

Contribution

It provides a comprehensive expression for the sequences for all real parameters and discusses their pre-classicality and implications for time asymmetry.

Findings

Sequences exhibit time asymmetry around the singularity

Derived explicit expressions for sequences for all real parameters

Sequences' behavior influences understanding of classical singularity

Abstract

In this paper, we discuss the properties of one-parameter sequences that arise when solving the Hamiltonian constraint in Bianchi I loop quantum cosmology using a separation of variables method. In particular, we focus on finding an expression for the sequence for all real values of the parameter, and discuss the pre-classicality of this function. We find that the behavior of these preclassical sequences imply time asymmetry on either side of the classical singularity in Bianchi I cosmology.