Loop quantum cosmology of k=1 FLRW: Effects of inverse volume corrections

TL;DR

This paper investigates the effects of inverse volume corrections in loop quantum cosmology for the closed FLRW model, demonstrating that these corrections ensure bounded energy density and expansion, thus improving the model's physical viability.

Contribution

It introduces and analyzes inverse volume corrections in the k=1 FLRW model within loop quantum cosmology, addressing issues of unbounded physical quantities.

Findings

Inverse corrections lead to bounded energy density near the bounce.

The quantum Hamiltonian constraint's self-adjointness is established for different quantizations.

Effective theories show improved physical behavior with inverse corrections.

Abstract

We consider the k=1 Friedman-Lemaitre-Robertson-Walker (FLRW) model within loop quantum cosmology (LQC), from the perspective of the two available quantization prescriptions. We focus our attention on the existence of the so called `inverse corrections' in the quantization process. We derive the corresponding quantum constraint operators, and study in detail the issue of the self-adjointness of the quantum Hamiltonian constraint for two different quantizations based on open holonomies. Furthermore, we analize in detail the resulting effective theories, paying special attention to issues such as the boundedness of different scalar observables such as energy density and expansion. We show that the inclusion of the inverse corrections solves one of the main undesirable features of the previous formalism, namely the unboundedness of the energy density and expansion near the bounce on the full (effective) phase space. We briefly comment on possible consequences of this new feature.