Super-exponential Primordial Black Hole Production via Delayed Vacuum Decay

TL;DR

This paper investigates how delayed vacuum decay during a slow cosmological phase transition can produce primordial black holes with a super-exponential dependence on model parameters, affecting their abundance.

Contribution

It introduces a simple model demonstrating the super-exponential dependence of black hole production on Euclidean action, and analyzes effects of modified expansion rates on this process.

Findings

Black hole abundance depends super-exponentially on Euclidean action.

Modified expansion rates weaken but do not eliminate the super-exponential dependence.

Results generalize to various frameworks of 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.