Loop Quantum Cosmology III: Wheeler-DeWitt Operators

TL;DR

This paper develops anomaly-free Wheeler-DeWitt operators within loop quantum cosmology for symmetric models, introducing new regularization techniques that respect the models' special structures and are applicable to various symmetric cases.

Contribution

It presents a novel construction of Wheeler-DeWitt operators in loop quantum cosmology that accounts for symmetry-specific features and extends to non-homogeneous models.

Findings

Constructed anomaly-free Hamiltonian constraint operators for symmetric models.

Introduced a new regularization procedure using point holonomies.

Applicable to both homogeneous and certain non-homogeneous models.

Abstract

In the framework of loop quantum cosmology anomaly free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop quantum gravity can be used, but there are also further inputs because the special structure of symmetric models has to be respected by operators. In particular, the basic building blocks of the homogeneous models are point holonomies rather than holonomies necessitating a new regularization procedure. In this respect, our construction is applicable also for other (non-homogeneous) symmetric models, e.g. the spherically symmetric one.