  Cosmic rays of the highest energy, above the Greisen-Zatsepin-Kuzmin cut-off
of the spectrum, may originate in decays of superheavy long-living X-particles.
These particles may be produced in the early Universe from vacuum fluctuations
during or after inflation and may constitute a considerable fraction of Cold
Dark Matter. We calculate numerically their abundance for a wide range of
models. X-particles are considered to be either bosons or fermions. Particles
that are several times heavier than inflaton, m_inflaton \approx 10^{13} GeV,
and were produced by this mechanism, can account for the critical mass in the
Universe naturally. In some cases induced isocurvature density fluctuations can
leave an imprint in anisotropy of cosmic microwave background radiation.
