Generalised constraints on the curvature perturbation from primordial
  black holes
  Primordial black holes (PBHs) can form in the early Universe via the collapse
of large density perturbations. There are tight constraints on the abundance of
PBHs formed due to their gravitational effects and the consequences of their
evaporation. These abundance constraints can be used to constrain the
primordial power spectrum, and hence models of inflation, on scales far smaller
than those probed by cosmological observations. We compile, and where relevant
update, the constraints on the abundance of PBHs before calculating the
constraints on the curvature perturbation, taking into account the growth of
density perturbations prior to horizon entry. We consider two simple
parameterizations of the curvature perturbation spectrum on the scale of
interest: constant and power-law. The constraints from PBHs on the amplitude of
the power spectrum are typically in the range 10^{-2}-10^{-1} with some scale
dependence.
