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. These light PBHs may be originated when a sizable comoving curvature perturbation generated during inflation reenters 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 a millihertz, 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.
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We warmly thank the anonymous referee and A. Lewis for asking about the propagation effect, which has led to the revised version. We also thank A. Lewis for input about the nonmeasurability of the bispectrum. N. B. acknowledges partial financial support by the ASI/INAF Agreement No. I/072/09/0 for the Planck LFI Activity of Phase E2. He also acknowledges financial support by ASI Grant No. 2016-24-H.0. A. R. is supported by the Swiss National Science Foundation (SNSF), project The Non-Gaussian Universe and Cosmological Symmetries, Project No. 200020-178787. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science.
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