An Investigation of Spontaneous Lorentz Violation and Cosmic Inflation

Abstract

In this thesis we re-examine two established ideas in theoretical physics: Lorentz invariance and cosmic inflation. In the first four chapters, we (i) propose a way to hide large extra dimensions by coupling standard model fields with Lorentz-violating tensor fields with expectation values along the extra dimensions; (ii) examine the stability of theories in which Lorentz invariance is spontaneously broken by fixed-norm `aether' fields; (iii) investigate the phenomenological properties of the sigma-model aether theory; and (iv) explore the implications of an alternative theory of gravity in which the graviton arises from the Goldstone modes of a two-index symmetric aether field. In the final chapter, we examine the horizon and flatness problems using the canonical measure (developed by Gibbons, Hawking, and Stewart) on the space of solutions to Einstein's equations. We find that the flatness problem does not exist, while the homogeneity of our universe does represent a substantial fine-tuning. Based on the assumption of unitary evolution (Liouville's theorem), we further dispute the widely accepted claim that inflation makes our universe more natural.