Dust reference frame in quantum cosmology

TL;DR

This paper introduces a quantum cosmology framework using pressureless dust as a reference frame, resulting in a simplified Schrödinger equation that enhances analysis in Wheeler-deWitt and loop quantum cosmology models.

Contribution

It presents a novel formulation with a linear Hamiltonian constraint in dust momentum, enabling a natural time gauge and broadening LQC applicability.

Findings

Unitary evolution linked to geodesic completeness

Simplified analysis of Wheeler-deWitt and LQC models

Applicable to arbitrary scalar potentials and cosmological constants

Abstract

We give a formulation of quantum cosmology with a pressureless dust and arbitrary additional matter fields. The system has the property that its Hamiltonian constraint is linear in the dust momentum. This feature provides a natural time gauge, leading to a physical hamiltonian that is not a square root. Quantization leads to Schr{\"o}dinger equation for which unitary evolution is directly linked to geodesic completeness. Our approach simplifies the analysis of both Wheeler-deWitt and loop quantum cosmology (LQC) models, and significantly broadens the applicability of the latter. This is demonstrated for arbitrary scalar field potential and cosmological constant in LQC.