Field-theoretic derivation of bubble-wall force

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