Matter Creation via Vacuum Fluctuations in the Early Universe and   Observed Ultra-High Energy Cosmic Ray Events
  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. 
V. A. Kuzmin and I. I. Tkachev