Inhomogeneous bubble nucleation in cosmological phase transitions using physics-informed neural networks

First-order phase transitions (FOPTs) in the early Universe are an object of worldwide research in the field of cosmology. Within FOPT models, one of the central tasks is the computation of the Euclidean action for the false vacuum decay. However, arriving at a numerical result using conventional methods can be difficult. In recent years, machine learning has been shown to be highly effective in solving this issue, whether by allowing to obtain the Euclidean action directly from the potential, or to retrieve the tunneling profiles. Here, we continue these efforts. We construct a physics-informed neural network (PINN) capable of solving the equation of motion for bubble configurations, and compare the results with existing profile solvers. Further, we apply the framework to the problem of bubble nucleation on topological defects, and explore the temperature dependence of the action. We contrast the findings with the case of standard homogeneous phase transition. Lastly, we discuss the challenges of generalization, that is, accuracy and reliability of the PINN on data outside the training set. This work provides a contemporary example of how PINNs can help manage the cumbersome computations encountered in cosmological phase transition models.