Lattice refinement in loop quantum cosmology

TL;DR

This paper discusses the importance of lattice refinement in loop quantum cosmology, demonstrating its role in inflationary models, presenting a numerical solution method, and establishing a unique factor ordering in the continuum limit.

Contribution

It introduces a numerical technique for solving the constraint equation with lattice refinement and shows how this leads to a unique factor ordering in the Wheeler-De Witt equation.

Findings

Lattice refinement is crucial for successful inflationary models.

A simple numerical method for solving the constraint equation is proposed.

Only a specific lattice refinement choice yields a unique factor ordering.

Abstract

Lattice refinement in LQC, its meaning and its necessity are discussed. The r\^ole of lattice refinement for the realisation of a successful inflationary model is explicitly shown. A simple and effective numerical technique to solve the constraint equation for any choice of lattice refinement model is briefly illustrated. Phenomenological and consistency requirements leading to a particular choice of lattice refinement model are presented, while it is subsequently proved that only this choice of lattice refinement leads to a unique factor ordering in the Wheeler-De Witt equation, which is the continuum limit of LQC.