Investigating Graviton Dynamics During the Electroweak Transition

Abstract

Understanding gravitational perturbations is the key to much of our knowledge of the early universe. In this thesis, we explore the dynamics of gravitons in the context of the electroweak transition, using scalar electrodynamics as a toy model. We want to find the equations of motion that govern the evolution of gravitational perturbations in an expanding universe, where we model matter as a thermal plasma. We follow a framework established by Liu and Prokopec by developing the equations of motion for the background as well as the graviton self-energy. Our goal is to discover whether the electroweak transition generates a graviton mass by changing the energy contents of the vacuum. We calculate the vacuum contribution to the self-energy, and we find that by using suitable counterterms the graviton remains massless both before and after the transition. We discuss how one could calculate the thermal corrections as well, which can be used to solve the perturbation equation of motion.