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

12 pages; v2: journal version, minor clarifications

References in corpus (10)

• Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology
• Instabilities in Mimetic Matter Perturbations
• Quanta of Geometry: Noncommutative Aspects
• Hypersurface-deformation algebroids and effective space-time models
• Effective loop quantum cosmology as a higher-derivative scalar-tensor theory
• Hamiltonian Formulation of Mimetic Gravity
• Loop Quantum Cosmology: A brief review
• Canonical Analysis of Inhomogeneous Dark Energy Model and Theory of Limiting Curvature
• Effective Actions from Loop Quantum Cosmology: Correspondence with Higher Curvature Gravity
• A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables

Cited by in corpus (25)

• Critical evaluation of common claims in loop quantum cosmology
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
• Higher Derivative Mimetic Gravity
• A no-go result for covariance in models of loop quantum gravity
• Cosmological perturbations and stability of nonsingular cosmologies with limiting curvature
• Cuscuton gravity as a classically stable limiting curvature theory
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Non-covariance of the dressed-metric approach in loop quantum cosmology
• Limiting curvature mimetic gravity and its relation to Loop Quantum Cosmology
• The singularity in mimetic Kantowski-Sachs cosmology
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Is limiting curvature mimetic gravity an effective polymer quantum gravity?
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Limiting curvature mimetic gravity for group field theory condensates
• Disforming to Conformal Symmetry
• Loop quantum gravity, signature change, and the no-boundary proposal
• Bouncing cosmologies via modified gravity in the ADM formalism: Application to Loop Quantum Cosmology
• Effective Field Theory of Loop Quantum Cosmology
• Theories with limited extrinsic curvature and a nonsingular anisotropic universe
• The Dapor-Liegener model of Loop Quantum Cosmology: A dynamical analysis
• Inequivalence of mimetic gravity with models of loop quantum gravity
• Physical Hamiltonian for mimetic gravity
• Holographic Signatures of Resolved Cosmological Singularities II: Numerical Investigations
• Dimensional aspects of Lovelock-Lanczos gravity