Field-theoretic derivation of bubble-wall force
  We derive a general quantum field theoretic formula for the force acting on
expanding bubbles of a first order phase transition in the early Universe
setting. In the thermodynamic limit the force is proportional to the entropy
increase across the bubble of active species that exert a force on the bubble
interface. When local thermal equilibrium is attained, we find a strong
friction force which grows as the Lorentz factor squared, such that the bubbles
quickly reach stationary state and cannot run away. We also study an opposite
case when scatterings are negligible across the wall (ballistic limit), finding
that the force saturates for moderate Lorentz factors thus allowing for a
runaway behavior. We apply our formalism to a massive real scalar field, the
standard model and its simple portal extension. 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.
