Lensing by primordial black holes: constraints from gravitational wave
  observations
  Primordial black holes (PBHs) have been proposed to explain at least a
portion of dark matter. Observations have put strong constraints on PBHs in
terms of the fraction of dark matter which they can represent, $f_{\rm PBH}$,
across a wide mass range -- apart from the stellar-mass range of
$20M_\odot\lesssim M_{\rm PBH}\lesssim 100M_\odot$. In this paper, we explore
the possibility that such PBHs could serve as point-mass lenses capable of
altering the gravitational-wave (GW) signals observed from binary black hole
(BBH) mergers along their line-of-sight. We find that careful GW data analysis
could verify the existence of such PBHs based on the $fitting~factor$ and odds
ratio analyses. When such a lensed GW signal is detected, we expect to be able
to measure the redshifted mass of the lens with a relative error $\Delta M_{\rm
PBH}/M_{\rm PBH}\lesssim0.3$. If no such lensed GW events were detected despite
the operation of sensitive GW detectors accumulating large numbers of BBH
mergers, it would translate into a stringent constraint of $f_{\rm PBH}\lesssim
10^{-2}-10^{-5}$ for PBHs with a mass larger than $\sim10M_\odot$ by the
Einstein Telescope after one year of running, and $f_{\rm PBH}\lesssim 0.2$ for
PBHs with mass greater than $\sim 50M_\odot$ for advanced LIGO after ten years
of running.
