Understanding the dynamics strong first order electroweak transitions is important as the resulting gravitational wave observations by LISA can be used to improve our understanding of the physics at the electroweak scale and beyond. In this talk I will explain how to obtain a general, quantum field theoretic, formula for the force acting on an expanding bubbles at a first order electroweak transition. In the thermodynamic limit the force is proportional to the entropy increase across the bubble and when local thermal equilibrium is attained, the force grows as the Lorentz factor squared, such that the bubbles cannot run away. We apply our formalism to a real scalar field toy model, to the standard model and to its simple portal extension. We also compare with the existing literature, and find that bubbles can run away if scatterings are negligible across the wall (ballistic limit), but they always reach a stationary limit with a finite Lorentz factor if scatterings are efficient across the bubble. For completeness, we also present a derivation of the renormalized, one-loop, thermal energy-momentum tensor for the standard model and demonstrate its gauge independence.
This seminar is based on https://arxiv.org/pdf/2005.10875.pdf.