New Hamiltonians for loop quantum cosmology with arbitrary spin representations

TL;DR

This paper introduces a new polynomial Hamiltonian formula for flat FLRW models in loop quantum cosmology using arbitrary spin representations, addressing an important ambiguity and exploring its physical implications.

Contribution

It provides a closed-form, polynomial Hamiltonian for arbitrary spin representations, unifying regularization schemes and incorporating inverse-volume corrections in loop quantum cosmology.

Findings

Derived a new closed formula for Hamiltonians with arbitrary spin

Analyzed the effective classical dynamics and stability of difference equations

Studied the impact of increasing spin representations on critical density

Abstract

In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity whose understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat FLRW models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased, and the stability of the difference equations in the quantum theory.