Detecting the gravitational wave background from primordial black hole
  dark matter
  The black hole merging rates inferred after the gravitational-wave detection
by Advanced LIGO/VIRGO and the relatively high mass of the progenitors are
consistent with models of dark matter made of massive primordial black holes
(PBH). PBH binaries emit gravitational waves in a broad range of frequencies
that will be probed by future space interferometers (LISA) and pulsar timing
arrays (PTA). The amplitude of the stochastic gravitational-wave background
expected for PBH dark matter is calculated taking into account various effects
such as initial eccentricity of binaries, PBH velocities, mass distribution and
clustering. It allows a detection by the LISA space interferometer, and
possibly by the PTA of the SKA radio-telescope. Interestingly, one can
distinguish this background from the one of non-primordial massive binaries
through a specific frequency dependence, resulting from the maximal impact
parameter of binaries formed by PBH capture, depending on the PBH velocity
distribution and their clustering properties. Moreover, we find that the
gravitational wave spectrum is boosted by the width of PBH mass distribution,
compared with that of the monochromatic spectrum. The current PTA constraints
already rule out broad-mass PBH models covering more than three decades of
masses, but evading the microlensing and CMB constraints due to clustering.
