Uncertainties in primordial black-hole constraints on the primordial power spectrum

Abstract

The existence (and abundance) of primordial black holes (PBHs) is governed by the power spectrum of primordial perturbations generated during inflation. So far no PBHs have been observed, and instead, increasingly stringent bounds on their existence at different scales have been obtained. Up until recently, this has been exploited in attempts to constrain parts of the inflationary power spectrum that are unconstrained by cosmological observations. We first point out that the simple translation of the PBH non-observation bounds into constraints on the primordial power spectrum is inaccurate as it fails to include realistic aspects of PBH formation and evolution. We then demonstrate, by studying two examples of uncertainties from the effects of critical and non-spherical collapse, that even though they may seem small, they have important implications for the usefulness of the constraints. In particular, we point out that the uncertainty induced by non-spherical collapse may be much larger than the difference between particular bounds from PBH non-observations and the general maximum cap stemming from the condition $\Omega \leq 1$ on the dark-matter density in the form of PBHs. We therefore make the cautious suggestion of applying only the overall maximum dark-matter constraint to models of early Universe, as this requirement seems to currently provide a more reliable constraint, which better reflects our current lack of detailed knowledge of PBH formation. These, and other effects, such as merging, clustering and accretion, may also loosen constraints from non-observations of other primordial compact objects such as ultra-compact minihalos of dark matter.