Primordial Black Holes as Dark Matter
  The possibility that the dark matter comprises primordial black holes (PBHs)
is considered, with particular emphasis on the currently allowed mass windows
at $10^{16}$ - $10^{17}\,$g, $10^{20}$ - $10^{24}\,$g and $1$ -
$10^{3}\,M_{\odot}$. The Planck mass relics of smaller evaporating PBHs are
also considered. All relevant constraints (lensing, dynamical, large-scale
structure and accretion) are reviewed and various effects necessary for a
precise calculation of the PBH abundance (non-Gaussianity, non-sphericity,
critical collapse and merging) are accounted for. It is difficult to put all
the dark matter in PBHs if their mass function is monochromatic but this is
still possible if the mass function is extended, as expected in many scenarios.
A novel procedure for confronting observational constraints with an extended
PBH mass spectrum is therefore introduced. This applies for arbitrary
constraints and a wide range of PBH formation models, and allows us to identify
which model-independent conclusions can be drawn from constraints over all mass
ranges. We focus particularly on PBHs generated by inflation, pointing out
which effects in the formation process influence the mapping from the
inflationary power spectrum to the PBH mass function. We then apply our scheme
to two specific inflationary models in which PBHs provide the dark matter. The
possibility that the dark matter is in intermediate-mass PBHs of $1$ -
$10^{3}\,M_{\odot}$ is of special interest in view of the recent detection of
black-hole mergers by LIGO. The possibility of Planck relics is also intriguing
but virtually untestable.
