Anomaly freedom in perturbative loop quantum gravity

TL;DR

This paper develops a consistent linear perturbation theory in loop quantum gravity that incorporates quantum corrections without breaking space-time covariance, linking fundamental quantum effects to cosmological phenomenology.

Contribution

It introduces a method to include quantum corrections in cosmological perturbation theory within loop quantum gravity while maintaining anomaly-free constraints.

Findings

Quantum corrections can be incorporated without spoiling covariance.

Constraint algebra remains consistent with quantum modifications.

Provides a framework connecting quantum gravity and cosmological observations.

Abstract

A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, non-trivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed insights for the correct implementation of constraint operators can be gained. The procedures of this article thus provide a clear link between fundamental quantum gravity and phenomenology.