Consequences of regularization ambiguities in Loop Quantum Cosmology

TL;DR

This paper examines the effects of regularization ambiguities in Loop Quantum Cosmology, focusing on the third quantization prescription, analyzing its mathematical properties, dynamics, and comparing it with other approaches.

Contribution

It provides a detailed analysis of the third regularization prescription (mLQC-II) in Loop Quantum Cosmology, expanding understanding of its mathematical and dynamical properties.

Findings

The quantum Hamiltonian constraint operator has well-defined mathematical properties.

The system's evolution is uniquely determined under the studied prescription.

Comparison shows distinct features of mLQC-II relative to other prescriptions.

Abstract

Ambiguities of the so-called Thiemann regularization in Loop Quantum Cosmology lead to freedom in how to construct a particular quantization prescription. So far three distinct examples of such have been proposed in the literature. For two of them, detailed analysis has been already performed in the literature. In this thesis, the methodology developed for these is applied to study in detail the third one, which will be referred to as mLQC-II. In particular, the mathematical properties of the operator of the quantum version of full Hamiltonian constraint are examined. These properties indicate that the evolution of the system is uniquely determined. Furthermore, an investigation of dynamics is performed by finding the expectation value of the volume as a function of the scalar field and constants of motion. This result is next compared to the trajectories predicted with the so-called effective dynamics. Finally, the main properties of studied prescription are compared against those of other (already investigated) ones.