How to Calculate the Bubble Nucleation Rate in First Order Transitions Non-perturbatively

Electroweak baryogenesis in the Standard Model (or extensions of it) happens on or near the surface of the bubbles which nucleate and subsequently grow during the first order Electroweak phase transition. In this case, it is very difficult to compute the bubble nucleation rate analytically with sufficient accuracy: since the transition is radiatively generated, no classical bubble solution exists, and the whole idea of separating the classical bubble from the fluctuation determinant, needed for Langer’s nucleation theory, becomes cumbersome. Furthermore, the long-distance physics of the Electroweak theory is inherently non-perturbative, making lattice simulations necessary. How can one calculate the nucleation rate on the lattice? The most straightforward method is to take an ensemble of configurations in the metastable state, evolve each with Hamilton’s equations of motion, and wait for tunneling to happen. This has been done, for instance in the Ising model and the φ model. However, the cooling rate of the Universe during the Electroweak phase transition is many orders of magnitude smaller than the timescale of microscopic interactions. Thus, the system has plenty of time for probing its phase space, and the tunneling will happen through very strongly suppressed configurations (p ∼ e) after a small amount of supercooling. However, it is impossible to make Monte Carlo simulations with e iterations! Below, we shall describe a Monte Carlo method which fully overcomes this problem, and which can be used to calculate both the static and the dynamical parts of the nucleation rate. Instead of using the full SU(2) × U(1)+Higgs,