Approximate Canonical Quantization for Cosmological Models

TL;DR

This paper introduces an approximate quantization scheme for complex cosmological models that are nonintegrable and not exactly solvable, utilizing gauge-invariant quantities to facilitate the process.

Contribution

It proposes a novel method for quantizing perturbed, nonintegrable cosmological models using approximate gauge invariants, expanding the tools for quantum cosmology.

Findings

Successfully applied to simple quantum cosmological models

Provides a framework for approximate quantization of nonintegrable systems

Enhances understanding of quantum behavior in complex cosmological scenarios

Abstract

In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this in mind, we present a scheme for the (approximate) quantization of perturbed, nonintegrable, time-reparametrization invariant systems that uses (approximate) gauge invariant quantities. We apply the scheme to a couple of simple quantum cosmological models.