Pitfalls of a power-law parameterization of the primordial power
  spectrum for Primordial Black Hole formation
  Primordial Black Holes (PBHs) can form in the radiation dominated early
Universe from the collapse of large density perturbations produced by
inflation. A power-law parameterisation of the primordial power spectrum is
often used to extrapolate from cosmological scales, where the amplitude of the
perturbations is well-measured by Cosmic Microwave Background and Large Scale
Structure observations, down to the small scales on which PBHs may form. We
show that this typically leads to large errors in the amplitude of the
fluctuations on small scales, and hence extremely inaccurate calculations of
the abundance of PBHs formed.
