Robust $\mu$-distortion constraints on primordial supermassive black holes from non-Gaussian perturbations

TL;DR

This paper establishes new constraints on primordial supermassive black hole formation considering non-Gaussian perturbations, showing that certain high-order non-Gaussianities could enable black hole formation without violating spectral distortion limits.

Contribution

First robust constraints on primordial black hole formation with large non-Gaussianity, extending previous Gaussian-based limits and exploring extreme non-Gaussian models.

Findings

Infinite $f_{NL}$ non-Gaussianity is insufficient for black hole formation.

High-order non-Gaussianity of the form ${ m R}={ m R}_G^5$ can allow black hole formation.

Extreme models face additional challenges beyond spectral distortion constraints.

Abstract

Explaining the origin of supermassive black holes via a primordial origin is severely challenged by the tight spectral distortion constraints on the amplitude of the primordial perturbations. Following the first calculation of how the $\mu$ constraints are modified by non-Gaussianity in a companion paper, we here make the first robust constraints on primordial black hole formation under large non-Gaussianity. Even the infinite $f_{\rm NL}$ limit is insufficiently non-Gaussian but much higher-order non-Gaussianity of the form ${\cal R}={\cal R}_{\rm G}^5$ may allow the formation of any mass primordial black hole without conflicting with distortion constraints. We caution that such extreme models face other challenges.