Detecting dark matter substructures on small scales with fast radio bursts

The matter power spectrum is only weakly constrained on subgalactic scales, while physics beyond the Standard Model can leave unique imprints, especially on sub-parsec scales. We propose measuring the arrival-time difference of fast radio bursts (FRBs) along two adjacent sightlines as a new probe to dark matter substructures on scales down to $\sim 1\mathrm{AU}$. We discuss two observational scenarios in which it may be possible to place interesting constraints on such models through the monitoring of repeating FRB sources: (i) By sending radio receivers to space to form a baseline of tens of AU or more and measuring the temporal variation of the arrival-time difference between receivers. (ii) By measuring the temporal variation of the arrival-time difference between two lensed images of one strongly lensed repeater. In both scenarios, obtaining interesting constraints requires correlating the voltage time series to measure the radio signal arrival time to sub-nanosecond precision. We find that two radio dishes separated by 20 AU may be sensitive to the enhancement of small-scale structures at $\sim {10}^{-8}{M}_{\odot }$ masses in the QCD axion dark matter scenario, or from an early epoch of matter domination with a reheating temperature up to 60 MeV. Other dark matter models, such as those composed of $\sim {10}^{-13}{M}_{\odot }$ primordial black holes produced during inflation, would also be probed by this method. We further show that a strong lensing situation of multiple images provides an equivalent $\sim 2000\mathrm{AU}({\sigma }_v/{10}^3\mathrm{km}{s}^{-1})(\delta t/10\mathrm{yr})$ baseline, for a typical velocity of dark matter substructures ${\sigma }_v$ and an observational time span $\delta$. This is much more sensitive, but with the uncertainty that intervening decoherence from the interstellar medium may degrade the timing precision, and that spatial variation in the FRB emission spot may result in confounding signals. We show that the lensing magnifications of Type Ia supernovae constrain a similar quantity to such FRB timing, with present limits being equivalent to ruling out the same parameter space that would be probed by a 0.14 AU baseline.