Power spectrum of density fluctuations, halo abundances and clustering
  with primordial black holes
  We study the effect of dark matter (DM) being encapsulated in primordial
black holes (PBHs) on the power spectrum of density fluctuations $P(k)$; we
also look at its effect on the abundance of haloes and their clustering. We
allow the growth of Poisson fluctuations since matter and radiation equality
and study both monochromatic and extended PBH mass distributions. We present
updated monochromatic black hole mass constraints by demanding $<10\%$
deviations from the $\Lambda$ cold dark matter power spectrum at a scale of
$k=1$hMpc$^{-1}$. Our results show that PBHs with masses $>10^4$h$^{-1}M_\odot$
are excluded from conforming all of the DM in the Universe. We also apply this
condition to our extended Press-Schechter (PS) mass functions, and find that
the Poisson power is scale dependent even before applying evolution. We find
that characteristic masses $M^*\leq10^2 $h$^{-1}M_\odot$ are allowed, {leaving
only two characteristic PBH mass windows of PS mass functions when combining
with previous constraints, at $M^*\sim10^2$h$^{-1}M_\odot$ and
$\sim10^{-8}$h$^{-1}M_\odot$ where all of the DM can be in PBHs. The resulting
DM halo mass functions within these windows are similar} to those resulting
from cold dark matter made of fundamental particles. However, as soon as the
parameters produce unrealistic $P(k)$, the resulting halo mass functions and
their bias as a function of halo mass deviate strongly from the behaviour
measured in the real Universe.
