Higgsless Simulations of Relativistic Hydrodynamics and Gravitational Wave Production in Cosmological Phase Transitions

This thesis explores the production of gravitational waves (GWs) during first-order cosmological phase transitions (PTs) and presents the core findings from my doctoral research. Central to my work is the development of a novel simulation framework that leverages a Higgsless approach specifically designed to model the relativistic hydrodynamics and GW production associated with such transitions.The Higgsless simulations introduce a highly efficient method designed to capture the nonlinear dynamics of the primordial fluid, offering precise extraction of GW spectra from first-order PTs. By excluding the Higgs field dynamics, the simulations achieve significant computational cost reduction without sacrificing accuracy, making it a valuable tool for further progress within the field and the broader community.Our Higgsless approach has proven exceptionally effective at solving the relativistic hydrodynamic equations with great precision, resolving high-gradient phenomena such as shocks and nonlinear evolution - critical for accurate GW predictions - while maintaining computational efficiency. The Higgsless approach, therefore, effectively bridges the gap between the traditional semianalytic models and computationally expensive numerical simulations.This thesis is divided into two main sections. Part I offers a concise theoretical foundation on GWs and PTs in cosmology, setting the stage for the subsequent scientific investigations. Part II delves into key theoretical concepts for numerical simulations, including central difference methods, before detailing the implementation, validation, and application of the Higgsless simulations. These simulations serve as the foundation for the thesis's primary results and scientific contributions.Major achievements of my research include the development of a 3D, fully nonlinear hydrodynamical simulation code for modeling PT dynamics using the Higgsless approach. This innovation enabled novel predictions of GW production driven by fluid dynamics in PTs, marking the first-ever derivation of GW spectra from strong PTs. Additionally, it provided detailed insights into the parametric dependence of the GW spectrum on fundamental PT quantities across a broad range of the PT parameters space.