  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.
