  We propose a model where a long-lived pseudoscalar EeV particle can be
produced with sufficient abundance so as to account for the cold dark matter
density, despite having a Planck mass suppressed coupling to the thermal bath.
Connecting this state to a hidden sterile neutrino sector through derivative
couplings, induced by higher dimensional operators, allows one to account for
light neutrino masses while having a lifetime that can be much larger than the
age of the Universe. Moreover, the same derivative coupling accounts for the
production of dark matter in the very first instant of the reheating. Given the
sensitivity of the IceCube and ANITA collaborations, we study the possible
signatures of such a model in the form of Ultra-High-Energy Cosmic Rays in the
neutrino sector, and show that such signals could be detected in the near
future.
