Is Dark Matter the Relic of the Primordial Matter That Created the Visible Matter of the Universe?

Quantum field theory in nonstationary curved Friedmann spacetime leads to the phenomenon of massive particles creation. The hypothesis that, at the end of inflation, gravitation creates from vacuum superheavy particles as some primordial matter decaying into quarks and leptons, leading to the observed baryonic charge, is investigated. Taking a complex scalar field for these particles, by analogy with K-0 meson theory, one obtains two components, the long- and short-lived ones, so that the long- lived component, after breaking the Grand Unification symmetry, has a long lifetime and is observed today as dark matter. The hypothesis, that ultra-high energy cosmic rays occur as a manifestation of superheavy dark matter, is considered, and some experimental possibilities of the proposed scheme are analyzed. Some new results on nonconformal scalar particle creation are presented.