Reflections on Bubble Walls

We discuss the dynamics of expanding bubble walls in the presence of massive dark photons whose mass changes as they cross the wall. For suﬃciently thin walls, we show that there exists a transient kinematic regime characterized by a constant reﬂection probability of longitudinal – but not transverse – modes. This eﬀect can have important implications for the dynamics of expanding vacuum bubbles in the early Universe. Most notably, it leads to a new source of pressure on the expanding interface, featuring a non-monotonic dependence on the γ -factor of the bubble walls and reaching a peak at intermediate γ -factors that we dub Maximum Dynamic Pressure. When this pressure is large enough to halt the acceleration of the bubble walls, the diﬀerence in vacuum energy densities goes into making a fraction of the dark photons relativistic, turning them into dark radiation. If the dark radiation remains relativistic until late times, an observable contribution to ∆ N eﬀ is possible for phase transitions with strength α ∼ 10 − 2 − 10 − 1 . (Dated