Approaches To Quantum Cosmology: A Review

TL;DR

This review explores the path integral approach to quantum cosmology, detailing derivations of wavefunctions from Euclidean and Lorentzian actions, and comparing with canonical quantisation methods for minisuperspace models.

Contribution

It provides a comprehensive comparison of path integral and canonical quantisation techniques in quantum cosmology, including new calculations for matter- and radiation-dominated universes.

Findings

Derivation of Hartle-Hawking and Vilenkin wavefunctions from Euclidean and Lorentzian actions

Path integral quantisation of Einstein-Cartan action for minisuperspace models

Complementary results to canonical quantisation approaches

Abstract

A review of the path integral approach to quantum cosmology and its relation to canonical quantisation. The initial derivation of the Hartle-Hawking and Vilenkin wavefunctions from the Euclidean Einstein-Hilbert action, and later, from the Lorentzian path integral using Picard-Lefshets Theory is discussed. Path integral quantisation of the Einstein-Cartan action is then employed to obtain the wavefunctions for minisuperspace closed FRW universes dominated by matter and radiation. These calculations are complimentary to those recently carried out by Magueijo using canonical quantisation of the same action.