Deriving the initial conditions of the electroweak and QCD phase transitions and testing a numerical relativity code.

The field of Numerical Relativity (NR) has been primarily driven by the study of largescale dynamics involving binary systems of black holes and neutron stars. Due to the nature of the underlying theory, NR also has the ability to simulate relativistic fluids. Being radiation dominated, the early universe can be modeled as a relativistic plasma, and the proper Stress-Energy tensor can be utilized with Einstein’s Field Equations to evolve the conditions of the Early Universe over time. These simulations can give us key insights pertaining to the development of the universe and the formation of large-scale systems. Magnetogenesis is of particular interest, as characterizing this phenomenon could shed light on the seeding and formation of galaxies. Addition-ally, these techniques can be used to derive gravitational-wave spectra from the events that took place during these time periods. This thesis aims to derive the conditions present in the early universe during the Electroweak (EW) and Quantum Chromodynamic (QCD) phase transitions. These conditions are prerequisites for SpecCosmo, a NR code being developed at the University of Houston-Clear Lake, which utilizes the techniques of NR to model the evolution of the early universe. This thesis will also investigate the ability of SpecCosmo to handle relativistic shocks in its current state. The shock capturing ability of the code will be gauged using a suite of tests from work by Komissarov [1, 2]. Once the shock capturing ability of SpecCosmo has been analyzed, SpecCosmo will be ready to accept the initial conditions calculated here that can then be used in simulations of the early universe to study its development and characteristics.