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

@article{Bodendorfer2018CanonicalSO, title={Canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity}, author={Norbert Bodendorfer and Andreas Schafer and John Schliemann}, journal={Physical Review D}, year={2018}, volume={97}, pages={084057} }

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…

## 31 Citations

Is limiting curvature mimetic gravity an effective polymer quantum gravity?

- PhysicsClassical and Quantum Gravity
- 2018

A recently proposed version of mimetic gravity incorporates a limiting curvature into general relativity by means of a specific potential depending on the d’Alembertian of the scalar field. In the…

No-go result for covariance in models of loop quantum gravity

- Physics
- 2020

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…

Limiting curvature mimetic gravity and its relation to Loop Quantum Cosmology

- PhysicsGeneral Relativity and Gravitation
- 2019

Considering as usual that the underlying geometry of our universe is well described by the spatially flat Friedmann–Lemaître–Robertson–Walker line element, we review how the background of holonomy…

Limiting extrinsic curvature theory and stable non-singular anisotropic universe

- Physics
- 2020

We propose a class of theories that can limit scalars constructed from the extrinsic curvature. Applied to cosmology, this framework allows us to control not only the Hubble parameter but also…

Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2018

We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which…

Theories with limited extrinsic curvature and a nonsingular anisotropic universe

- Physics
- 2020

We propose a class of theories that can limit scalars constructed from the extrinsic curvature. Applied to cosmology, this framework allows us to control not only the Hubble parameter but also…

Physical Hamiltonian for mimetic gravity

- Physics
- 2020

Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $\phi$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in…

Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity

- PhysicsUniverse
- 2019

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f(□ϕ)…

Effective Field Theory of Loop Quantum Cosmology

- PhysicsUniverse
- 2019

Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty…

Limiting curvature mimetic gravity for group field theory condensates

- PhysicsPhysical Review D
- 2019

Nonsingular bouncing cosmologies are realized in limiting curvature mimetic gravity by means of a multi-valued potential $f(\Box\phi)$ depending on the d'Alembertian of a scalar field $\phi$. We…

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