Axion Dynamics Across First-Order Phase Transitions

In this work, we study axion dynamics during first-order phase transitions and investigate the bubble misalignment mechanism. First, we review the evidence for dark matter at different scales and explore various dark matter production mechanisms, including thermal and non-thermal relics. Then, we discuss the key theoretical framework of quantum field theory at finite temperature to understand phase transitions in the early universe, with specific attention to bubble nucleation and expansion processes that characterize first-order transitions. We then introduce the axion as a solution to the strong CP problem and explore its properties, interactions, and production processes, including the conventional misalignment mechanism. The main focus of this work is to analyze the bubble misalignment mechanism, in which axions interact with expanding bubble walls during a first-order phase transition. We classify different dynamical regimes based on the hierarchy between the Hubble parameter, axion masses, and phase transition duration. Through analytical calculations and numerical simulations, we demonstrate that axion waves undergo Fermi acceleration when reflecting off the bubble walls, eventually gaining sufficient energy to penetrate the bubbles. This mechanism modifies the axion abundance and momentum distribution compared to standard scenarios. Finally, our novel analysis of multiple bubble simulations shows how the number density of axions scales with the bubble wall velocity and bubble number with important implications for the axion dark matter abundance. These results contribute to our understanding of axion dynamics in the early universe and may have implications for the parameter space of axion searches.