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The highest energy cosmic rays, above the Greisen-Zatsepin-Kuzmin cut-off ofcosmic ray spectrum, may be produced in decays of superheavy long-livingX-particles. We conjecture that these particles may be produced naturally inthe early Universe from vacuum fluctuations during inflation and may constitutea considerable fraction of Cold Dark Matter. We predict a new cut-off in theUHE cosmic ray spectrum E_{cut-off} < m_inflaton \approx 10^{13} GeV, the exactposition of the cut-off and the shape of the cosmic ray spectrum beyond the GZKcut-off being determined by the QCD quark/gluon fragmentation. The Pierre AugerProject installation might discover this phenomenon.Comment: LaTeX, 8 page

Ultrahigh-energy cosmic rays, superheavy long-lived particles, and matter creation after inflation