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.

中文翻译：

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气泡壁力的场论推导

我们推导出了一个通用的量子场论公式，用于在早期宇宙环境中作用于一阶相变的膨胀气泡上的力。在热力学极限中，力与在气泡界面上施加力的活性物质穿过气泡的熵增加成正比。当达到局部热平衡时，我们发现一个强大的摩擦力，它随着洛伦兹因子的平方而增长，使得气泡迅速达到静止状态并且无法逃跑。我们还研究了一个相反的情况，当穿过墙壁的散射可以忽略不计（弹道极限）时，发现力对于中等洛伦兹因子饱和，从而允许失控行为。我们将我们的形式主义应用于一个巨大的实标量场、标准模型及其简单的门户扩展。为了完整性，