All Dark Matter as Primordial Black Holes: a Gravitational-Wave Test

We propose a novel test for the hypothesis that the dark matter of the Universe is composed entirely by asteroidal-mass primordial black holes. It relies on detecting the stochastic gravitational-wave background generated by the coalescence onto rapidly spinning supermassive astrophysical black holes of the light primordial black holes accumulated in spherically symmetric spikes. We discuss the scenarios in which the signal can be observed by the future space-based gravitational-wave observatories LISA and DECIGO.