Remarks on the Bojowald--Paily paper Deformed general relativity

TL;DR

This paper critically examines the technical details of a previous work on deformed general relativity derived from loop quantum gravity, questioning the validity of key formulas and their implications.

Contribution

It provides a detailed critique of the explicit formula and the embedding approach in the original paper, highlighting potential oversimplifications and raising conceptual questions.

Findings

The explicit formula for the deformation function may be oversimplified.

The embedding of deformed special relativity in deformed general relativity is problematic.

Questions are raised about the consistency of the proposed models.

Abstract

A couple of technicalities in the paper M. Bojowald, G. Paily, Phys. Rev. D 87, 044044 (2013) are discussed. The explicit formula given there for the function entering the modified hypersurface-deformed algebra, which presumably originates in loop quantum gravity, seems to be oversimplified, and the embedding of deformed special relativity in deformed general relativity proposed there for spherically symmetric models raises some questions as well.