Constraint on the abundance of primordial black holes in dark matter
  from Planck data
  We use Planck data released in 2015 to constrain the abundance of primordial
black holes (PBHs) in dark matter in two different reionization models (one is
the instantaneous reionization and the other is the asymmetric reionization),
and significantly improve the upper limits on the abundance of PBHs from WMAP
3-year data by around two orders of magnitude. Furthermore, these new limits
imply that the event rates of mergers of PBH binaries (Gpc$^{-3}$ yr$^{-1}$)
are less than $0.002$ for $M_\text{pbh}=30M_\odot$, $5$ for
$M_\text{pbh}=10M_\odot$ and $2000$ for $M_\text{pbh}=2M_\odot$ at $95\%$
confidence level (C.L.), and thus GW150914 seems very unlikely produced by the
merger of a PBH binary.
