Precise LIGO Lensing Rate Predictions for Binary Black Holes
  We show how LIGO is expected to detect coalescing binary black holes at
$z>1$, that are lensed by the intervening galaxy population. Gravitational
magnification, $\mu$, strengthens gravitational wave signals by $\sqrt{\mu}$,
without altering their frequencies, which if unrecognised leads to an
underestimate of the event redshift and hence an overestimate of the binary
mass. High magnifications can be reached for coalescing binaries because the
region of intense gravitational wave emission during coalescence is so small
($\sim$100km), permitting very close projections between lensing caustics and
gravitational-wave events. Our simulations incorporate accurate waveforms
convolved with the LIGO power spectral density. Importantly, we include the
detection dependence on sky position and orbital orientation, which for the
LIGO configuration translates into a wide spread in observed redshifts and
chirp masses. Currently we estimate a detectable rate of lensed events
\rateEarly{}, that rises to \rateDesign{}, at LIGO's design sensitivity limit,
depending on the high redshift rate of black hole coalescence.
