Phase Transitions in the Early Universe

I explore the theory and computation of early-Universe finite-temperature phase transitions involving scalar fields. I focus primarily on the electroweak phase transition, but some of the methods I develop are applicable to any scalar-field cosmological phase transition (such as the computation of the lifetime of zero-temperature metastable vacua). I begin by examining phase transition thermodynamics with many extra coupled degrees of freedom, finding that such transitions have the potential to produce large amounts of entropy and can significantly dilute the concentration of thermal relic species (e.g., dark matter). I then detail a novel algorithm for calculating instanton solutions with multiple dynamic scalar fields, and present a computational package which implements the algorithm and computes the finite-temperature phase structure. Next, I discuss theoretical and practical problems of gauge dependence in finite-temperature effective potentials, using the Abelian Higgs and Abelian Higgs plus singlet models to show the severity of the problem. Finally, I apply the aforementioned algorithm to the electroweak phase transition in the next-to-minimal supersymmetric standard model (NMSSM). My collaborators and I find viable regions of the NMSSM which contain a strongly first-order phase transition and large enough CP violation to support electroweak baryogenesis, evade electric dipole moment constraints, and provide a dark matter candidate which could produce the observed 130 GeV gamma-ray line observed in the galactic center by the Fermi Gamma-ray Space Telescope