Super-exponential Primordial Black Hole Production via Delayed Vacuum Decay

Abstract: If a cosmological first-order phase transition occurs sufficiently slowly, delayed vacuum decay may lead to the formation of primordial black holes. Here we consider a simple model as a case study of how the abundance of the produced black holes depends on the model's input parameters. We demonstrate, using both numerical and analytical arguments and methods, that the black hole abundance is controlled by a double, ``super''-exponential dependence on the three-dimensional Euclidean action over temperature at its minimal value. We show that a modified expansion rate during the phase transition, such as one driven by an additional energy density component, leads to a weaker dependence on the underlying model parameters, but maintains the same super-exponential structure. We argue that our findings generalize to any framework of black hole production via delayed vacuum decay.