Date of Award

7-15-2026

Document Type

Thesis

Degree Name

MSc by Research in Natural Sciences

First Advisor

Dr. Kazuyuki Furuuchi

Abstract

This thesis explores the fundamental boundary conditions of the universe within the framework of canonical quantum cosmology, critically examin-ing the mathematical prescriptions that dictate its initial state. Central to this work is a comparative analysis of the Hartle-Hawking No-Boundary proposal and Vilenkin's Tunneling solution. While the Hartle-Hawking Eu-clidean path integral elegantly replaces the initial singularity with a smooth geometric cap, semiclassical approximations reveal a severe phenomeno-logical flaw: it exponentially favors a low-energy, empty universe over the high-energy state required to trigger slow-roll inflation. To resolve this, the study evaluates Vilenkin's Tunneling solution, which enforces an outgoing-wave boundary condition that naturally favors a high-initial-energy density. The thesis subsequently applies Vilenkin's quantum creation framework to establish the initial boundary conditions for chain inflation. By modeling early-universe expansion as a rapid sequence of microscopic quantum tun-neling events across a complex scalar field potential landscape, this work demonstrates how Vilenkin's boundary conditions successfully initiate the inflationary cascade. The continuous thermalization generated by these se-quential transitions is shown to naturally bypass the classical graceful exit problem, offering a mathematically consistent model for both the universe's quantum nucleation and its subsequent macroscopic evolution.

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