Anomaly freedom in perturbative models of Euclidean loop quantum gravity

TL;DR

This paper investigates the consistency of anomaly-free scalar perturbation models in Euclidean loop quantum gravity, highlighting differences in holonomy modifications and comparing various effective and operator approaches.

Contribution

It introduces a specific form of holonomy modification and analyzes its impact on anomaly freedom, providing a comparative study of different models in Euclidean LQG.

Findings

Constraint brackets are deformed differently than in previous models

Overall consistency found between effective and operator approaches

Holonomy modifications can be implemented without anomalies

Abstract

Euclidean gravity provides an interesting test system for an analysis of cosmological perturbations in an effective Hamiltonian constraint with holonomy modifications from loop quantum gravity. This paper presents a discussion of scalar modes, with a specific form of the holonomy modification function derived from a general expansion in a connection formulation. Compared with some previous models, the constraint brackets are deformed in a different and more restricted way. A general comparison of anomaly-free brackets in various effective and operator versions shows overall consistency between different approaches.