Unstable Anisotropic Loop Quantum Cosmology

TL;DR

This paper investigates the stability of the quantum dynamics in anisotropic loop quantum cosmology, revealing potential instabilities that challenge current quantization methods and their connection to full loop quantum gravity.

Contribution

It provides a stability analysis of the Hamiltonian constraint in anisotropic LQC, highlighting issues with the difference equation implementation and implications for quantization choices.

Findings

Evidence of instability in the difference equation

Implications for quantization approach and lattice refinement

Questions about the role of ambiguity parameters

Abstract

We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of LQC. Our analysis has shown robust evidence of an instability in the explicit implementation of the difference equation, implying important consequences for the correspondence between the full LQG theory and LQC. As a result, one may question the choice of the quantisation approach, the model of lattice refinement, and/or the role of the ambiguity parameters; all these should in principle be dictated by the full LQG theory.