Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems

TL;DR

This paper analyzes a simplified loop quantum cosmology model of diagonal Bianchi type I, highlighting analytical control and numerical evolution, but also identifying scaling issues that challenge the physical interpretation of the model.

Contribution

It constructs a simplified $ar{3}$ scheme-based model of diagonal Bianchi I in loop quantum cosmology and discusses its analytical and numerical properties, revealing scaling problems.

Findings

Numerical nonsingular evolution of gravitational degrees of freedom is achievable.

The naive $ar{3}$ scheme implementation faces invariance and scaling issues.

Scaling problems hinder the extraction of physical predictions from the model.

Abstract

A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to the $\bar{\mu}$ scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of the $\bar{\mu}$ scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes serious problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of the $\bar{\mu}$ scheme to the Bianchi I model do not imply limitations of the $\bar{\mu}$ scheme in the isotropic case.