The Probability for Primordial Black Holes

TL;DR

This paper explores the quantum cosmological probability of primordial black holes forming from scalar fields, finding that only Planck-sized black holes are unsuppressed initially, with potential growth during scalar field evolution.

Contribution

It introduces a quantum cosmological framework for analyzing primordial black hole formation using the Hartle-Hawking no-boundary proposal.

Findings

Black holes start at Planck size with high probability.

Black holes can grow during scalar field evolution.

Only Planck-sized black holes are initially unsuppressed.

Abstract

We consider two quantum cosmological models with a massive scalar field: an ordinary Friedmann universe and a universe containing primordial black holes. For both models we discuss the complex solutions to the Euclidean Einstein equations. Using the probability measure obtained from the Hartle-Hawking no-boundary proposal, we find that the only unsuppressed black holes start at the Planck size but can grow with the horizon scale during the roll down of the scalar field to the minimum.