In this lecture we conjecture that the Ultra-High Energy Cosmic Rays (UHECR) with energies E>EGZK, where EGZK∼5⋅1019eV is the Greisen-Zatsepin-Kuzmin cut-off energy of cosmic ray spectrum, may originate from decays of superheavy long-living X-particles populating the Universe thus providing a unique window into the very early epoch of the Universe, namely, that of preheating and reheating after inflation. These particles may constitute a considerable fraction of cold dark matter in the Universe. We argue that the unconventionally long lifetime of the superheavy particles, which should be in the range of 1010–1022 years, might require novel particle physics mechanisms of their decays, such as instantons. First of all I will describe a toy model illustrating the instanton scenario and then will describe the possible proper mechanism of creation of superheavy particles in the early Universe. It is my pleasure to emphasize that all I will talk about was done in collaboration with my friends V. A. Rubakov and I. I. Tkachev.

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