Ultra-High Energy Cosmic Rays, Superheavy Long-Living Particles, and Matter Creation after Inflation

The highest energy cosmic rays, above the Greisen-Zatsepin-Kuzmin cut-off of cosmic ray spectrum, may be produced in decays of superheavy long-living X-particles. We conjecture that these particles may be produced naturally in the early Universe from vacuum fluctuations during inflation and may constitute a considerable fraction of Cold Dark Matter. We predict a new cut-off in the UHE cosmic ray spectrum E_{cut-off} < m_inflaton \approx 10^{13} GeV, the exact position of the cut-off and the shape of the cosmic ray spectrum beyond the GZK cut-off being determined by the QCD quark/gluon fragmentation. The Pierre Auger Project installation might discover this phenomenon.