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.
@article{arxiv.1809.04465,
title = {Anomaly freedom in perturbative models of Euclidean loop quantum gravity},
author = {Jian-Pin Wu and Martin Bojowald and Yongge Ma},
journal= {arXiv preprint arXiv:1809.04465},
year = {2018}
}