Shortcomings of the Big Bounce derivation in Loop Quantum Cosmology

TL;DR

This paper discusses the definition of the electric field operator in Loop Quantum Gravity for cosmology, highlighting issues with the super-Hamiltonian regularization due to the discrete spectrum of the area operator.

Contribution

It provides a new prescription for defining the electric field operator in Loop Quantum Cosmology and explores its implications for the theory's consistency.

Findings

The electric field operator can be linked to the scale factor in homogeneous isotropic models.

The area operator has a discrete spectrum in Loop Quantum Cosmology.

Super-Hamiltonian regularization remains an open issue due to these spectral properties.

Abstract

We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time. This procedure allows to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in Loop Quantum Cosmology. This feature makes the super-Hamiltonian regularization an open issue of the whole formulation.