Hypersurface-deformation algebroids and effective space-time models

TL;DR

This paper explores how hypersurface-deformation algebroids relate different quantum gravity models to classical space-time, revealing signature change as a unique quantum phenomenon and identifying additional quantum corrections.

Contribution

It introduces a framework using Lie algebroid morphisms to connect various quantum-modified brackets to classical structures, highlighting the emergence of signature change as a quantum effect.

Findings

Signature change is a generic feature of quantum corrections.

Classical space-time structures are recovered in low-curvature regimes.

Additional quantum corrections beyond previous models are identified.

Abstract

In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie algebroid morphisms therefore allow one to relate different versions of the brackets that correspond to the same space-time structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can in some cases map the space-time structure back to the classical Riemannian form after a field redefinition. For one type of quantum corrections (holonomies), signature change appears to be a generic feature of effective space-time, and is shown here to be a new quantum space-time phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions prove the existence of classical space-time structures assumed elsewhere in models of loop quantum cosmology, but also shows the existence of additional quantum corrections that have not always been included.