Cold Dark Matter, Radiative Neutrino Mass, mu to e gamma, and Neutrinoless Double Beta Decay

Two of the most important and pressing questions in cosmology and particle physics are: (1) What is the nature of cold dark matter? and (2) Will near-future experiments on neutrinoless double beta decay be able to ascertain that the neutrino is a Majorana particle, i.e. its own antiparticle? We show that these two seemingly unrelated issues are intimately connected if neutrinos acquire mass only because of their interactions with dark matter.