Reverse direct detection: Cosmic ray scattering with light dark matter

Sub-GeV dark matter candidates are of increasing interest, because long-favored candidates such as GeV-scale weakly interacting massive particles have not been detected. For low-mass dark matter, model-independent constraints are weak or nonexistent. We show that for such candidates, because the number density is high, cosmic ray propagation can be affected by elastic scattering with dark matter. We call this type of search reverse direct detection, because dark matter is the target and standard model particles are the beam. Using a simple propagation model for galactic cosmic rays, we calculate how dark matter affects cosmic ray spectra at Earth, and set new limits on the dark matter-proton and dark matter-electron cross sections. For protons, our limit is competitive with cosmological constraints, but is independent. For electrons, our limit covers masses not yet probed, and improves on cosmological constraints by one to two orders of magnitude. We comment on how future work can significantly improve the sensitivity of cosmic-ray probes of dark matter interactions.