Approaches To Quantum Cosmology: A Review

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.