Non-covariance of "covariant polymerization" in models of loop quantum gravity

TL;DR

This paper investigates whether certain modifications inspired by loop quantum gravity preserve general covariance, revealing that some do not and introducing new physical effects like time-reversal hypersurfaces.

Contribution

It demonstrates that non-bijective canonical transformations in loop quantum gravity models do not necessarily preserve general covariance, challenging assumptions about their invariance.

Findings

Non-bijective transformations do not preserve general covariance.

Time-reversal hypersurfaces are introduced by certain modifications.

Canonical transformations require space-time analysis to verify covariance.

Abstract

It is possible to implement a certain form of modified gravity inspired by loop quantization through non-bijective canonical transformations. The canonical nature might suggest that such modifications are guaranteed to preserve general covariance. Here, however, we show that a dedicated space-time analysis is still required, even in the case of a bijective canonical transformation. In addition, a complete global analysis is presented for a recent proposal of a non-bijective transformation, showing that it does not preserve general covariance and that the only novel physical effect introduced by the modification is the presence of certain time-reversal hypersurfaces between classical space-time regions. These results provide further insights into the physical interpretation of modified dynamics in models of loop quantum gravity.