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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2018
 DOI:
 10.1088/13616382/aae74b
 arXiv:
 arXiv:1806.02052
 Bibcode:
 2018CQGra..35v5001B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 13 pages