The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology

TL;DR

This paper investigates how quantum geometry operators behave in Loop Quantum Cosmology, showing they can characterize physical solutions and retain many properties from the kinematical level, thus clarifying their role in the dynamical sector.

Contribution

It extends the analysis of quantum geometry in Loop Quantum Gravity to the cosmological model, deriving partial observables in both kinematical and physical Hilbert spaces.

Findings

Quantum geometry operators characterize physical solutions.

Operators preserve many kinematical properties.

Analysis is based on the isotropic universe model.

Abstract

This letter is motivated by the recent papers by Dittrich and Thiemann and, respectively, by Rovelli discussing the status of Quantum Geometry in the dynamical sector of Loop Quantum Gravity. Since the papers consider model examples, we also study the issue in the case of an example, namely on the Loop Quantum Cosmology model of space-isotropic universe. We derive the Rovelli-Thiemann-Ditrich partial observables corresponding to the quantum geometry operators of LQC in both Hilbert spaces: the kinematical one and, respectively, the physical Hilbert space of solutions to the quantum constraints. We find, that Quantum Geometry can be used to characterize the physical solutions, and the operators of quantum geometry preserve many of their kinematical properties.