Hubble operator in isotropic loop quantum cosmology

TL;DR

This paper constructs a Hubble operator within isotropic loop quantum cosmology, demonstrating its role as a Dirac observable and revealing a generic superinflation phase through expectation value analysis.

Contribution

It introduces a new Hubble operator in loop quantum cosmology that is invariant on physical solutions and exhibits superinflation behavior.

Findings

Hubble operator constructed as a Dirac observable

Operator's expectation value indicates superinflation phase

Dynamical selection of physical solution subspace

Abstract

We present a construction of the Hubble operator for the spatially flat isotropic loop quantum cosmology. This operator is a Dirac observable on a subspace of the space of physical solutions. This subspace gets selected dynamically, requiring that its action be invariant on the physical solution space. As a simple illustrative application of the expectation value of the operator, we do find a generic phase of (super)inflation, a feature shown by Bojowald from the analysis of effective Friedmann equation of loop quantum cosmology.