Are Primordial Black Holes Truly Fine-Tuned?

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 standardly 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 well-defined indicator of fine-tuning should assign large values to scenarios requiring significant parameter adjustment to reproduce the desired primordial black hole abundance, while yielding values of order unity in cases governed by standard 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.