An introduction to quantum cosmology

TL;DR

This paper provides an introductory overview of quantum cosmology, covering its theoretical foundations, quantisation methods, boundary conditions, and key predictions about the early universe and its evolution.

Contribution

It offers a comprehensive introduction to quantum cosmology, including historical context, mathematical formulations, and discussions of boundary proposals and their implications.

Findings

Discussion of the no-boundary and tunneling proposals

Insights into the origin of density perturbations

Predictions about the inflationary period and arrow of time

Abstract

This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A brief history of quantum cosmology. 2. Hamiltonian formulation of general relativity: 2.1 The 3+1 decomposition; 2.2 The action. 3. Quantisation: 3.1 Superspace; 3.2 Canonical quantisation; 3.3 Path integral quantisation; 3.4 Minisuperspace; 3.5 The WKB approximation; 3.6 Probability measures; 3.7 Minisuperspace for the Friedmann universe with massive scalar field. 4. Boundary Conditions: 4.1 The no-boundary proposal; 4.2 The tunneling proposal. 5. The predictions of quantum cosmology: 5.1 The period of inflation; 5.2 The origin of density perturbations; 5.3 The arrow of time.