Primordial black holes from single-field inflation: a fine-tuning audit

TL;DR

This paper evaluates the degree of fine-tuning required in single-field inflation models to produce primordial black holes, revealing that small parameter adjustments can significantly alter the predicted power spectrum and PBH abundance.

Contribution

It provides a quantitative analysis of the tuning necessary in inflationary potentials for PBH formation, highlighting the challenges in model construction.

Findings

Parameter changes of 1% to 10^-8 can alter the power spectrum peak amplitude by an order of magnitude.

Fine-tuning of PBH abundance exceeds 1-2 orders of magnitude.

Polynomial potentials require additional fine-tuning to match CMB observations.

Abstract

All single-field inflationary models invoke varying degrees of tuning in order to account for cosmological observations. Mechanisms that generate primordial black holes (PBHs) from enhancement of primordial power at small scales posit inflationary potentials that transiently break scale invariance and possibly adiabaticity over a range of modes. This requires additional tuning on top of that required to account for observations at scales probed by cosmic microwave background (CMB) anisotropies. In this paper we study the parametric dependence of various single-field models of inflation that enhance power at small scales and quantify the degree to which coefficients in the model construction have to be tuned in order for certain observables to lie within specified ranges. We find significant tuning: changing the parameters of the potentials by between one part in a hundred and one part in $10^8$ (depending on the model) is enough to change the power spectrum peak amplitude by an order one factor. The fine-tuning of the PBH abundance is larger still by 1-2 orders of magnitude. We highlight the challenges imposed by this tuning on any given model construction. Furthermore, polynomial potentials appear to require significant additional fine-tuning to also match the CMB observations.