Homeopathic Dark Matter, or how diluted heavy substances produce high energy cosmic rays

We point out that current and planned telescopes have the potential of probing annihilating Dark Matter (DM) with a mass of O(100) TeV and beyond. As a target for such searches, we propose models where DM annihilates into lighter mediators, themselves decaying into Standard Model (SM) particles. These models allow to reliably compute the energy spectra of the SM final states, and to naturally evade the unitarity bound on the DM mass. Indeed, long-lived mediators may cause an early matter-dominated phase in the evolution of the Universe and, upon decaying, dilute the density of preexisting relics thus allowing for very large DM masses. We compute this dilution in detail and provide results in a ready-to-use form. Considering for concreteness a model of dark U(1) DM, we then study both dilution and the signals at various high energy telescopes observing gamma rays, neutrinos and charged cosmic rays. This study enriches the physics case of these experiments, and opens a new observational window on heavy new physics sectors.