Topological defects in cosmology

Abstract

In this dissertation I use one dimensional numerical simulations of classical scalar field theories to study density of topological defects. I devise and compare three methods of counting defects and run multiple simulations with varying parameters. Thesis begins with general description of evolution of the Universe and how topological defects might have influenced it. This is followed by general mathematical description of Kibble-Zurek Mechanism (the mechanism that causes topological defects to form). In the first chapter I go through of all textbook theory regarding one dimensional field and defects needed to understand the model I am simulating, the model itself being a 1+1 dimensional scalar field theory with O(N) symmetry. In the second chapter I derive three methods for finding defects in the simulation data. In the third chapter I describe the simulations themselves and go through the immediate results. In the fourth chapter I discuss the results of the simulations and suggest future simulations in order to study this subject further. In the Appendix are exact results of simulations, more detailed derivation of certain equations and the simulation code written in pseudo-code.