Detecting Subsolar-Mass Primordial Black Holes in Extreme Mass-Ratio Inspirals with LISA and Einstein Telescope

Primordial black holes possibly formed in the early universe could provide a significant fraction of the dark matter and would be unique probes of inflation. A smoking gun for their discovery would be the detection of a subsolar mass compact object. We argue that extreme mass-ratio inspirals will be ideal to search for subsolar-mass black holes not only with LISA but also with third-generation ground-based detectors such as Cosmic Explorer and the Einstein Telescope. These sources can provide unparalleled measurements of the mass of the secondary object at subpercent level for primordial black holes as light as ${\cal O}(0.01)M_\odot$ up to luminosity distances around hundred megaparsec and few gigaparsec for LISA and Einstein Telescope, respectively, in a complementary frequency range. This would allow claiming, with very high statistical confidence, the detection of a subsolar-mass black hole, which would also provide a novel (and currently undetectable) family of sources for third-generation detectors.