Simulations of early universe phase transitions and gravitational waves

Upcoming space based gravitational wave observatories like the Laser Interferometer Space Antenna (LISA) will provide a new window into early universe physics. While the results from ground-based detectors have largely concerned astrophysical objects such as black holes and neutron stars, future space-based gravitational wave observatories will be able to observe far earlier times in the history of the universe than are directly accessible through the electromagnetic spectrum. LISA in particular will be sensitive to the detection of a stochastic gravitational wave background from a first-order cosmological phase transition around the electroweak scale. In cosmological phase transitions, an e?ective scalar field passes from a false vacuum state to the true vacuum. If the transition is first-order, this occurs through the nucleation of bubbles of the true vacuum. These bubbles expand and, upon collision, produce gravitational waves. The focus of this thesis is to better characterise the gravitational wave signal from a first-order phase transition using numerical simulations. Within this thesis, I study both vacuum and thermal first-order phase transitions. In a vacuum phase transition, bubble walls accelerate to ultra-relativistic speeds. In this case, the gradients in the scalar field during bubble collisions form the dominant source of gravitational waves. I perform full 3D classical lattice field theory simulations, compute the gravitational wave signature and compare it to previously used techniques such as the envelope approximation. I further extend this work to investigate whether the shape of the e?ective potential of the scalar field can a?ect the final gravitational wave signal. In thermal phase transitions, the bubbles of the true vacuum nucleate in the presence of a relativistic plasma. As the bubbles expand, friction between the outward propagating bubble wall and the plasma causes shells of fluid to form around the bubble wall. The dominant source of gravitational waves from thermal transitions is shear-stress that remains in the fluid after the transition completes. While simulations of weak and intermediate strength phase transitions have been conducted, I perform the first 3D simulations of a strongly first-order phase transition and provide results for the generation of vorticity, formation of heated droplets, and the e?ect that this has on the gravitational wave signal.