Nucleation Rate in a Radiatively Induced First-Order Phase Transition

We apply the modern effective field theory framework to study the nucleation rate in high-temperature first-order phase transitions. With this framework, an effective description for the critical bubble can be constructed, and the exponentially large contributions to the nucleation rate can then be computed from the effective description. The results can be used to make more accurate predictions relating to cosmological first-order phase transitions, for example, the gravitational wave spectrum from a transition, which is important for the planned experiment LISA. We start by reviewing a nucleation rate calculation for a classical scalar field to understand, how the critical bubble arises, via a saddle-point approximation, as the central object of the nucleation rate calculation. We then focus on the statistical part of the nucleation rate coming from the Boltzmann suppression of nucleating bubbles. This is done by the creation of an effective field theory from a thermal field theory that can describe the critical bubble. We give an example calculation with the renormalizable model of two $\mathbb{Z}_2$-symmetric scalar fields. The critical bubbles of the model and their Boltzmann suppression are studied numerically, for which we further develop a recently proposed method