# On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity

## TL;DR

This paper explores a modified general relativity with a limiting curvature, showing its connection to loop quantum gravity and analyzing its canonical structure to provide insights into quantum gravity models.

## Contribution

It analyzes the canonical structure of a limiting curvature gravity theory and clarifies its relation to loop quantum gravity in symmetric and full settings.

## Key findings

- Agreement with loop quantum gravity in symmetric sectors
- Extension to full general relativity without symmetry assumptions
- Insights into the canonical structure relevant for quantum gravity

## Abstract

Chamseddine and Mukhanov recently proposed a modified version of general relativity that implements the idea of a limiting curvature. In the spatially flat, homogeneous, and isotropic sector, their theory turns out to agree with the effective dynamics of the simplest version of loop quantum gravity if one identifies their limiting curvature with a multiple of the Planck curvature. At the same time, it extends to full general relativity without any symmetry assumptions and thus provides an ideal toy model for full loop quantum gravity in the form of a generally covariant effective action known to all orders. In this paper, we study the canonical structure of this theory and point out some interesting lessons for loop quantum gravity. We also highlight in detail how the two theories are connected in the spatially flat, homogeneous, and isotropic sector.