Pulsar Timing Array Constraints on the Induced Gravitational Waves
  If the black holes detected by LIGO/VIRGO are primordial black holes (PBHs)
sourcing from a large primordial curvature perturbation on small scales, the
corresponding induced gravitational waves (GWs) would peak at nanohertz that is
detectable by the current and future observations of pulsar timing array (PTA).
In this paper we show that with the mass function estimated from the merger
rate of LIGO O1 and O2 events, the induced GWs from such a curvature
perturbation with a Gaussian narrow peak at some small scale would be in a
seemingly mild tension with current constraints from PTA. However, if the
curvature perturbation is of local-type non-Gaussianity with a non-linear
parameter $f_\text{NL}\gtrsim\mathcal{O}(10)$, the tension could be relieved.
Nevertheless, such an induced GWs must be detectable by the Square Kilometer
Array in a decade or less.
