Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe

Phase transition dynamics may play important roles in the evolution history of the early universe, such as its possible roles in electroweak baryogenesis and dark matter. We systematically discuss and clarify the important details of the phase transition dynamics during a strong first-order phase transition (SFOPT). We classify the SFOPT into four types: slight supercooling, mild supercooling, strong supercooling, and ultra supercooling. Using different characteristic temperatures, length scales and bubble wall velocities, the corresponding gravitational wave (GW) spectra are investigated in details. We emphasize the essential importance of using the correct characteristic temperature and length scale when the phase transition dynamics and GW spectra are calculated. Especially, for strong supercooling and ultra supercooling cases, there are obvious differences of the phase transition strength and GW spectra between the results calculated at the nucleation temperature and those derived at the percolation temperature. For ultra supercooling case, we propose a criterion to quantify whether the phase transition can terminate. Besides the model-independent discussions, we also study three representative models as concrete examples to clearly show the subtle points therein.