Description
The possibility that future gravitational-wave detectors could observe the relic background of a cosmological phase transition has triggered intense progress in the theoretical description of these events. A detection of any such background can therefore probe energies far above those accessible to particle colliders, shedding light on fundamental physics questions, such as the state of the early Universe, the baryon asymmetry of the Universe, the nature of the dark matter, or whether exotic objects like primordial black holes or cosmic strings exist. First-order phase transitions proceed through the nucleation and expansion of bubbles, whose microscopic properties, such as the bubble nucleation rate, fluctuation determinants, and wall velocity, directly determine the resulting gravitational-wave spectrum. Reliable predictions therefore require a precise treatment of thermal field theory, out-of-equilibrium dynamics, and the interaction of the bubble wall with the primordial plasma. To enable systematic studies of models beyond the standard model, these developments must be automated and implemented in robust computational tools. Recent and forthcoming programs for determining bubble determinants and bubble-wall velocities represent important steps in this direction. I will review key advances in modelling phase-transition dynamics, discuss the challenges that remain, and outline how improved automation will sharpen gravitational-wave predictions for upcoming experiments.
