Gauge-invariant construction of quantum cosmology

TL;DR

This paper develops a gauge-invariant quantum cosmology model for a dust-filled universe, using relational formalism to construct a reduced phase space, which is then quantized to address the problem of time and avoid initial singularity.

Contribution

It introduces a gauge-invariant quantum framework for the Friedmann-Robertson-Walker universe using relational formalism, providing a novel approach to quantum cosmology.

Findings

Quantum effects avoid the classical initial singularity.

The reduced phase space can be quantized like a standard mechanical system.

The approach offers a resolution to the problem of time in quantum gravity.

Abstract

We present and analyze a gauge-invariant quantum theory of the Friedmann-Robertson-Walker universe with dust. We construct the reduced phase space spanned by gauge-invariant quantities by using the so-called relational formalism at the classical level. The reduced phase space thereby obtained can be quantized in the same manner as an ordinary mechanical system. We carry out the quantization and obtain the Schr\"{o}dinger equation. This quantization procedure realizes a possible resolution to the problem of time and observables in canonical quantum gravity. We analyze the classical initial singularity of the theory by evolving a wave packet backward in time and evaluating the expectation value of the scale factor. It is shown that the initial singularity of the Universe is avoided by the quantum gravitational effects.