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.