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All single-field inflationary models invoke varying degrees of tuning inorder to account for cosmological observations. Mechanisms that generateprimordial black holes (PBHs) from enhancement of primordial power at smallscales posit inflationary potentials that transiently break scale invarianceand possibly adiabaticity over a range of modes. This requires additionaltuning on top of that required to account for observations at scales probed bycosmic microwave background (CMB) anisotropies. In this paper we study theparametric dependence of various single-field models of inflation that enhancepower at small scales and quantify the degree to which coefficients in themodel construction have to be tuned in order for certain observables to liewithin specified ranges. We find significant tuning: changing the parameters ofthe 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 amplitudeby an order one factor. The fine-tuning of the PBH abundance is larger still by1-2 orders of magnitude. We highlight the challenges imposed by this tuning onany given model construction. Furthermore, polynomial potentials appear torequire significant additional fine-tuning to also match the CMB observations.

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