Probing Primordial-Black-Hole Dark Matter with Scalar Induced
  Gravitational Waves
  The possibility that primordial black holes (PBHs) represent all of the dark
matter (DM) in the Universe and explain the coalescences of binary black holes
detected by LIGO/Virgo has attracted a lot of attention. PBHs are generated by
the enhancement of scalar perturbations which inevitably produce the induced
gravitational waves (GWs). We calculate the induced GWs up to the third-order
correction which not only enhances the amplitude of induced GWs, but also
extends the cutoff frequency from $2k_*$ to $3k_*$. Such effects of the
third-order correction lead to an around $10\%$ increase of the signal-to-noise
ratio (SNR) for both LISA and pulsar timing array (PTA) observations, and
significantly widen the mass range of PBHs in the stellar mass window
accompanying detectable induced GWs for PTA observations including IPTA, FAST
and SKA. On the other hand, the null detections of the induced GWs by LISA and
PTA experiments will exclude the possibility that all of the DM is comprised of
PBHs and the GW events detected by LIGO/Virgo are generated by PBHs.
