Estimating the uncertainty of cosmological first order phase transitions with numerical simulations of bubble nucleation

In order to study the validity of analytical formulas used in the calculation of characteristic physical quantities related to vacuum bubbles, we conduct several numerical simulations of bubble kinematics in the context of cosmological first-order phase transitions to determine potentially existing systematic uncertainties. By comparing with the analytical results, we obtain the following observations: (1) The simulated false vacuum fraction will approach the theoretical one with increasing simulated volume. When the side length of the cubic simulation volume becomes larger than 14.5 beta(-1)(th), the simulated results do not change significantly. (2) The theoretical expected total number of bubbles do not agree with the simulated ones, which may be caused by the inconsistent use of the false vacuum fraction formula. (3) The different nucleation rate prefactors do not affect the bubble kinetics much. (4) The lifetime distribution in the sound shell model does not obey an exponential distribution, in such a way as to cause a suppression in the gravitational wave spectra.