Lattice Refining Loop Quantum Cosmology from an Isotropic Embedding of Anisotropic Cosmology

TL;DR

This paper presents a method to derive isotropic models from anisotropic Loop Quantum Cosmology, demonstrating lattice refinement through embeddings and introducing the concept of symmetric duals for step-size calculations.

Contribution

It introduces a novel approach for isotropic embedding of anisotropic models in Loop Quantum Cosmology, extending to three dimensions and defining symmetric duals for step-size determination.

Findings

Different isotropic embeddings can produce lattice refinement.

The method applies to both two- and three-dimensional anisotropic models.

Symmetric duals facilitate concise step-size calculations.

Abstract

We demonstrate that it is possible to produce different isotropic embeddings of anisotropic Loop Quantum Cosmology, resulting to "lattice refinement" in the isotropic system. To introduce the general approach, we first use a simple model with only two anisotropic directions. We then employ the specific case of a Bianchi I model, to show how the method extends to three-dimensional systems. To concisely calculate the step-size of the resulting isotropic state, we define the "symmetric dual" of states and operators, for the two- and three-dimensional systems, respectively.