Searching for near-horizon quantum structures in the binary black-hole
  stochastic gravitational-wave background
  It has been speculated that quantum gravity corrections may lead to
modifications to space-time geometry near black hole horizons. Such structures
may cause reflections to gravitational waves, causing {\it echoes} that follow
the main gravitational waves from binary black hole coalescence. We show that
such echoes, if exist, will give rise to a stochastic gravitational-wave
background, which is very substantial if the near-horizon structure has a near
unity reflectivity for gravitational waves, readily detectable by Advanced
LIGO. In case reflectivity is much less than unity, the background will mainly
be arising from the first echo, with a level proportional to the power
reflectivity of the near-horizon structure, but robust against uncertainties in
the location of the structure --- as long as it is very close to the horizon.
Sensitivity of third-generation detectors allows the detection of a background
that corresponds to power reflectivity $\sim 10^{-3}$, if the uncertainties in
the binary black-hole merger rate can be removed. We note that the echoes do
alter the $f^{2/3}$ power law of the background spectra at low frequencies,
which is rather robust against the uncertainties.
