Is limiting curvature mimetic gravity an effective polymer quantum gravity?

Abstract

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 homogeneous and isotropic setting, the resulting theory agrees with the simplest incarnation of effective loop quantum cosmology (LQC) once the limiting curvature is identified with a multiple of the Planck scale. In this paper, we answer the question of whether such a relation can hold in the context of Bianchi I models. Our result is negative: it turns out to be impossible to view the Hamiltonian of limiting curvature mimetic gravity as an effective LQC Hamiltonian due to the appearance of terms that cannot be supported on the polymer Hilbert space underlying LQC. The present analysis complements a related result in the context of spherical symmetry.

arXiv comment13 pages; v2: references added; v3: journal version, minor clarifications

References in corpus (22)

• The Dynamics of General Relativity
• Quantum Nature of the Big Bang: Improved dynamics
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Mimetic Dark Matter
• Loop quantum cosmology of Bianchi I models
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Polymer Quantum Mechanics and its Continuum Limit
• Loop quantization of the Schwarzschild interior revisited
• Nonsingular Black Hole
• Effective line elements and black-hole models in canonical (loop) quantum gravity
• Resolving Cosmological Singularities
• Bouncing cosmologies from quantum gravity condensates
• Why are the effective equations of loop quantum cosmology so accurate?
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
• Effective loop quantum cosmology as a higher-derivative scalar-tensor theory
• The loop quantum cosmology bounce as a Kasner transition
• A quantum reduction to Bianchi I models in loop quantum gravity
• On singularity-resolution in mimetic gravity
• Canonical Analysis of Inhomogeneous Dark Energy Model and Theory of Limiting Curvature
• On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity
• Effective Actions from Loop Quantum Cosmology: Correspondence with Higher Curvature Gravity

Cited by in corpus (16)

• Critical evaluation of common claims in loop quantum cosmology
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• A no-go result for covariance in models of loop quantum gravity
• 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
• Limiting curvature mimetic gravity for group field theory condensates
• Disforming to Conformal Symmetry
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Loop quantum gravity, signature change, and the no-boundary proposal
• Effective Field Theory of Loop Quantum Cosmology
• Theories with limited extrinsic curvature and a nonsingular anisotropic universe
• Inequivalence of mimetic gravity with models of loop quantum gravity
• Physical Hamiltonian for mimetic gravity
• Mimetic gravity: mimicking the dynamics of the primeval universe in the context of loop quantum cosmology