Field-theoretic derivation of bubble-wall force

Understand

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.