Is limiting curvature mimetic gravity an effective polymer quantum gravity?

TL;DR

This paper investigates whether limiting curvature mimetic gravity can be effectively described by polymer quantum gravity in Bianchi I models, concluding it cannot due to incompatible Hamiltonian structures.

Contribution

It demonstrates the incompatibility of limiting curvature mimetic gravity with effective loop quantum cosmology in anisotropic Bianchi I models.

Findings

Hamiltonian terms incompatible with polymer Hilbert space

No effective LQC description for limiting curvature mimetic gravity in Bianchi I

Supports previous results in spherical symmetry

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.