Primordial black hole dark matter from single field inflation

TL;DR

This paper introduces a single-field inflation model that produces primordial black holes in the mass range of 10^{-16} to 10^{-14} solar masses, potentially explaining dark matter, with detailed calculations showing the importance of accurate methods over slow-roll approximations.

Contribution

It presents a novel inflationary scenario with an inflection point from two-loop corrections, leading to efficient black hole production and precise abundance predictions.

Findings

Primordial black holes can account for a significant fraction of dark matter.

Accurate peak mass and abundance calculations require going beyond slow-roll approximation.

Predicted tensor spectrum may be detectable by future CMB experiments.

Abstract

We propose a model of inflation capable of generating a population of light black holes (about $10^{-16}$ - $10^{-14}$ solar masses) that might account for a significant fraction of the dark matter in the Universe. The effective potential of the model features an approximate inflection point arising from two-loop order logarithmic corrections in well-motivated and perturbative particle physics examples. This feature decelerates the inflaton before the end of inflation, enhancing the primordial spectrum of scalar fluctuations and triggering efficient black hole production with a peaked mass distribution. At larger field values, inflation occurs thanks to a generic small coupling between the inflaton and the curvature of spacetime. We compute accurately the peak mass and abundance of the primordial black holes using the Press-Schechter and Mukhanov-Sasaki formalisms, showing that the slow-roll approximation fails to reproduce the correct results by orders of magnitude. We study as well a qualitatively similar implementation of the idea, where the approximate inflection point is due to competing terms in a generic polynomial potential. In both models, requiring a significant part of the dark matter abundance to be in the form of black holes implies a small blue scalar tilt with a sizable negative running and a tensor spectrum that may be detected by the next-generation probes of the cosmic microwave background. We also comment on previous works on the topic.