Are Primordial Black Holes Truly Fine-Tuned?

TL;DR

This paper challenges the common criticism that primordial black hole models require excessive fine-tuning by proposing a new measure of naturalness, showing these models are not inherently unnatural.

Contribution

It introduces a modified Wilson's naturalness criterion to assess fine-tuning in primordial black hole models, providing a more balanced evaluation of their naturalness.

Findings

Primordial black hole models are not necessarily fine-tuned according to the new criterion.

The traditional measure of fine-tuning may overstate the unnaturalness of these models.

The new measure aligns the perceived naturalness with the actual sensitivity of the models.

Abstract

Single-field inflationary models which generate primordial black holes through the enhancement of the curvature primordial power at small scales are commonly criticized and frequently dismissed because they require a large amount of fine-tuning in the parameters setting the ultra slow-roll phase. However, the standarly adopted definition of fine-tuning has a clear drawback: the more the primordial black hole abundance is small and cosmologically harmless, the larger the parameter space is fine-tuned. A reliable measure of fine-tuning should deliver a large value when the primordial black hole abundance is fine-tuned and at the same time reduce to something close to unity when it encounters typical sensitivity. Motivated by such arguments, we use the (modified version of) Wilson's naturalness criterion for quantifying the fine-tuning and naturalness and we show that the primordial black hole models are not technically unnatural.