Prescriptions in Loop Quantum Cosmology: A comparative analysis

TL;DR

This paper compares different prescriptions in Loop Quantum Cosmology for quantizing flat homogeneous isotropic spacetimes, showing that while they agree on some observables, they differ significantly in wave function amplitudes at the bounce.

Contribution

It provides a detailed numerical comparison of various prescriptions in Loop Quantum Cosmology, highlighting their similarities and differences in quantum bounce behavior.

Findings

Expectations and dispersions are similar across prescriptions for non-deep quantum states.

Wave function amplitudes at the bounce differ significantly between prescriptions.

Simpler superselection sectors are more computationally efficient.

Abstract

Various prescriptions proposed in the literature to attain the polymeric quantization of a homogeneous and isotropic flat spacetime coupled to a massless scalar field are carefully analyzed in order to discuss their differences. A detailed numerical analysis confirms that, for states which are not deep in the quantum realm, the expectation values and dispersions of some natural observables of interest in cosmology are qualitatively the same for all the considered prescriptions. On the contrary, the amplitude of the wave functions of those states differs considerably at the bounce epoch for these prescriptions. This difference cannot be absorbed by a change of representation. Finally, the prescriptions with simpler superselection sectors are clearly more efficient from the numerical point of view.