We analyze Higgs condensate bubble expansion during a first-order electroweak phase transition in the early Universe. The interaction of particles with the bubble wall can be accompanied by the emission of multiple soft gauge bosons. When computed at fixed order in perturbation theory, this process exhibits large logarithmic enhancements which must be resummed to all orders when the wall velocity is large. We perform this resummation both analytically and numerically at leading logarithmic accuracy. The numerical simulation is achieved by means of a particle shower in the broken phase of the electroweak theory. The two approaches agree to the 10% level. For fast-moving walls, we find the scaling of the thermal pressure exerted against the wall to be P~γ²T⁴, independent of the particle masses, implying a significantly slower terminal velocity than previously suggested.

我们分析了在早期宇宙的一阶电弱相变过程中的希格斯凝结水气泡膨胀。粒子与气泡壁的相互作用可能伴随着多个软规格玻色子的发射。在微扰理论中以固定阶数计算时，此过程显示出较大的对数增强，当壁速较大时，必须将其恢复为所有阶数。我们以领先的对数精度在分析和数值上执行此恢复。数值模拟是通过在电弱理论的断裂相中进行粒子喷淋来实现的。两种方法均达到10％的水平。对于快速移动的壁，我们发现所施加靠墙为P〜γ的热压力的缩放² Ť ⁴，与颗粒质量无关，这意味着最终速度比以前建议的要慢得多。