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In the present paper, it is assumed that there exist two dark matterparticles: superheavy dark matter particles (SHDM), whose mass $\sim$ inflatonmass, and lighter fermion dark matter particles (LFDM) which are theultra-relativistic products of its decay. The event rates of LFDM measured bythe Pierre Auger observatory (Auger) are evaluated in the energy range between1 EeV and 1 ZeV at the zenith angles between 0$^{\circ}$ and 60$^{\circ}$ whenthe different lifetimes of decay of SHDM. Thus it is proved that thepossibility of measurement of these LFDM at Auger. Based on the assumption thatthe detection efficiency for a shower caused by LFDM is set to be 100\%, theLFDM contribution to the energy spectrum of extreme energy cosmic rays (EECRs)is discussed. And it is found that there are some hints on the existence ofSHDM and LFDM in the past EECRs observations.

Hints on the Existence of Superheavy Dark matter and Ultrahigh Energy Dark Matter in Extreme Energy Cosmic Rays Observations