Lensing of Fast Radio Bursts as a Probe of Compact Dark Matter

The possibility that part of the dark matter is made of massive compact halo objects (MACHOs) remains poorly constrained over a wide range of masses, and especially in the 20-100 M_{⊙} window. We show that strong gravitational lensing of extragalactic fast radio bursts (FRBs) by MACHOs of masses larger than ∼20 M_{⊙} would result in repeated FRBs with an observable time delay. Strong lensing of a FRB by a lens of mass M_{L} induces two images, separated by a typical time delay ∼few×(M_{L}/30 M_{⊙}) msec. Considering the expected FRB detection rate by upcoming experiments, such as canadian hydrogen intensity mapping experiment (CHIME), of 10^{4} FRBs per year, we should observe from tens to hundreds of repeated bursts yearly, if MACHOs in this window make up all the dark matter. A null search for echoes with just 10^{4} FRBs would constrain the fraction f_{DM} of dark matter in MACHOs to f_{DM}≲0.08 for M_{L}≳20 M_{⊙}.