  The idea that primordial black holes (PBHs) can comprise most of the dark
matter of the universe has recently reacquired a lot of momentum. Observational
constraints, however, rule out this possibility for most of the PBH masses,
with a notable exception around $10^{-12} M_\odot$. These light PBHs may be
originated when a sizeable comoving curvature perturbation generated during
inflation re-enters the horizon during the radiation phase. During such a
stage, it is unavoidable that gravitational waves (GWs) are generated. Since
their source is quadratic in the curvature perturbations, these GWs are
generated fully non-Gaussian. Their frequency today is about the mHz, which is
exactly the range where the LISA mission has the maximum of its sensitivity.
This is certainly an impressive coincidence. We show that this scenario of PBHs
as dark matter can be tested by LISA by measuring the GW two-point correlator.
On the other hand, we show that the short observation time (as compared to the
age of the universe) and propagation effects of the GWs across the perturbed
universe from the production point to the LISA detector suppress the bispectrum
to an unobservable level. This suppression is completely general and not
specific to our model.
