A no-go result for covariance in models of loop quantum gravity

TL;DR

This paper demonstrates that loop quantum cosmology modifications break general covariance in spherically symmetric models, indicating the need for a non-Riemannian geometry framework for consistent spacetime descriptions.

Contribution

It shows that loop quantum cosmology modifications cannot be embedded into covariant spherically symmetric theories, revealing a fundamental no-go result.

Findings

Loop quantum cosmology models violate slicing independence.

Covariant spherically symmetric theories cannot incorporate these modifications.

A non-Riemannian geometry may be necessary for consistent models.

Abstract

Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by symmetry-reduced models of quantum cosmology can be used to derive corresponding modified spherically symmetric equations. Generally covariant theories are much more restricted in spherical symmetry compared with homogeneous slicings, given by $1+1$-dimensional dilaton models if they are local. As shown here, modifications used in loop quantum cosmology do not have a corresponding covariant spherically symmetric theory. Models of loop quantum cosmology therefore violate general covariance in the form of slicing independence. Only a generalized form of covariance with a non-Riemannian geometry could consistently describe space-time in models of loop quantum gravity.