We study slow-down effects for bubbles formed in a cosmological first-order phase transition (PT) focusing on deflagrations and hybrids, where the bubble wall is preceded by a shockwave of heated plasma. Slow-down has been observed in multi-bubble simulations together with a suppression of gravitational wave (GW) emission, mostly for slow walls. We study the impact of the shock waves on the wall velocity around percolation, by considering steady-state single-bubble solutions and incorporating the possible heating effects by two different mechanisms. First, we investigate the slow-down experienced by a bubble expanding into an impeding shockwave, where the temperature is higher than at nucleation, and the fluid is no longer at rest. Taking into account such heating and kinematic effects, we find that the most significant slow-down occurs for the fastest walls, and thus cannot explain the suppression of the GWs observed in the simulations. However, these effects are stronger for PTs with a sizeable change in degrees of freedom unlike what is usually implemented in simulations, suggesting that the degrees of freedom can be an important additional parameter for characterizing the GW spectrum. For the second slow-down mechanism, we study heated droplets of false vacuum that shrink towards the end of the PT. By implementing a suitable boundary condition motivated by energy conservation, we show how the droplet velocity, interpreted here as the late-time velocity of the bubble walls, can be predicted from the properties of the initial deflagration/hybrid, in remarkable agreement with numerical simulations. Droplets are found to shrink more slowly for stronger PTs and slower deflagrations, with mild dependence on the change of degrees of freedom. Such slow droplets naturally correlate with a suppression of GWs, while geometrical properties such as the shock width play an important role as well.
Axion Misalignment Across First-Order Phase Transitions
Laboratory of High Energy and Computational Physics, NICPB（NICPB高能计算物理实验室）；Department of Cybernetics, Tallinn University of Technology（塔林理工大学网络学系）；Dipartimento di Fisica e Astronomia, Università degli Studi di Padova（帕多瓦大学物理与天文学系）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
Gravitational waves from strong first-order phase transitions in an expanding Universe
Chongqing University（重庆大学）；University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；International Center for Theoretical Physics Asia-Pacific（理论物理亚太中心）
Kobe University（神户大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大凌波书院）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
