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.
