Quantum cosmology

Abstract

This thesis investigates how the universe could have originated from a quantum state, following the Hartle–Hawking no-boundary proposal. We begin by examining the breakdown of classical general relativity near singularities such as the Big Bang. To move beyond these limitations, we turn to quantum cosmology and study the Wheeler–DeWitt equation, which governs the wave function of the universe. We explore this wave function using the minisuperspace approximation, a simplified model that reduces the complex dynamics to a few key variables. Within this framework, a Euclidean path integral is used to describe how the universe may have “tunneled” into existence from a quantum gravitational state. Focusing on the semiclassical limit, where quantum behavior transitions to classical dynamics, we analyze how a smooth, expanding universe like ours could emerge from these quantum origins.