Harvesting primordial black holes from stochastic trees with $\texttt{FOREST}$

TL;DR

This paper presents a new stochastic inflation framework using trees to model quantum diffusion and black hole formation, providing efficient simulations and detailed mass distributions of primordial black holes.

Contribution

Introduces the FOREST tool implementing stochastic trees for inflation modeling, capturing quantum effects and black hole formation more accurately than previous methods.

Findings

Primordial black holes form at unbalanced nodes of stochastic trees.

Mass distributions of black holes show broad, power-law-like profiles with exponential cutoffs.

The method automatically accounts for the cloud-in-cloud effect in black hole mass calculations.

Abstract

We introduce a novel framework to implement stochastic inflation on stochastic trees, modelling the inflationary expansion as a branching process. Combined with the $\delta N$ formalism, this allows us to generate real-space maps of the curvature perturbation that fully capture quantum diffusion and its non-perturbative backreaction during inflation. Unlike lattice methods, trees do not proceed on a fixed background since new spacetime units emerge dynamically as trees unfold, naturally incorporating metric fluctuations. The recursive structure of stochastic trees also offers remarkable numerical efficiency, and we develop the FOrtran Recursive Exploration of Stochastic Trees ($\texttt{FOREST}$) tool and demonstrate its performance. We show how primordial black holes blossom at unbalanced nodes of the trees, and how their mass distribution can be obtained while automatically accounting for the "cloud-in-cloud" effect. In the "quantum-well" toy model, we find broad mass distributions, with mild power laws terminated by exponential tails. We finally compare our results with existing approximations in the literature and discuss several prospects.