Non-standard loop quantum cosmology

TL;DR

This paper explores an alternative canonical quantization approach in loop quantum cosmology, analyzing the big bounce transition with a focus on the spectrum of the volume operator and its implications.

Contribution

It introduces a new canonical quantization method for LQC and investigates the spectral properties of the volume operator, providing insights into the quantum geometry of the big bounce.

Findings

The physical volume operator has a discrete, bounded spectrum.

A minimum gap in the spectrum defines a quantum of volume.

Spectra are parametrized by a free parameter to be determined.

Abstract

We present results concerning the nature of the cosmological big bounce(BB) transition within the loop geometry underlying loop quantum cosmology (LQC). Our canonical quantization method is an alternative to the standard LQC. An evolution parameter we use has clear interpretation both at classical and quantum levels. The physical volume operator has discrete spectrum which is bounded from below. The minimum gap in the spectrum defines a quantum of the volume. The spectra of operators are parametrized by a free parameter to be determined.