Oscillon Dynamics in Classical Scalar Field Theory

Abstract

Oscillons are spatially compact, temporally oscillatory, long-lived solutions to a non-linear wave equation. In this Thesis, we review the literature from both applied mathematics and physics on the subject of oscillon dynamics, and point out that the existing method of studying oscillon properties is not applicable to axion-monodromy oscillons, the understanding of which comprises the main goal of this project. Using the exact integrability of the 1D sine-Gordon equation, we construct an exact oscillon solution with two independent time-scales, named the “two-scale” solution, and numerically extend it to more general potentials and dimensionalities. We show that the novel field dynamics, namely the breathing modes and off-center peaks, is present in more general settings by proposing three numerical metrics capturing the essential field dynamics. Finally, we apply the exact two-scale solution to the axion-monodromy oscillons, in the setting of a post-inflationary universe, and conclude that the analytic ansatz obtained from the exact solution can account for local, but not global, breathing dynamics of the axion-monodromy oscillons in the very early universe.