Electroweak Phase Transition and Bubble Wall Velocity in Local Thermal Equilibrium

Abstract: The dynamics of the electroweak phase transition in the early universe has profound implications for cosmology and particle physics. We systematically study the steady-state dynamics of bubble walls in scenarios where the transition is first order within three representative beyond the Standard Model frameworks, characterised by the presence of an additional scalar in different electroweak representations. Focusing on the local thermal equilibrium regime, we numerically solve the coupled scalar and hydrodynamic equations to extract key properties of the phase transition front: the wall velocity, width, plasma and field profiles. Remarkably, we find a near-universal behaviour across models when expressed in terms of thermodynamic quantities, that can be captured by simple fitting functions, useful for phenomenological applications. These results also provide an upper bound on the bubble velocity and represent the first necessary step for the full inclusion of out-of-equilibrium effects.