Impossibility of strict thermodynamic equilibrium establishment in the accelerated Universe

In this article there are considered non-equilibrium cosmological scenarios with the assumption that scaling of particles interaction is restored in range of extra-high energies. On basis of energy-balance equation's exact solutions it is obtained the strong conclusion about fundamental unattainability of local thermodynamic equilibrium in the accelerated Universe. There are presented the results of numerical simulation of previously constructed strict mathematical model which describes thermodynamic equilibrium's establishment in the originally nonequilibrium cosmological ultrarelativistic plasma for the Universe with an arbitrary acceleration with the assumption that scaling of interactions of elementary particles is restored at energies above the unitary limit. Limiting parametres of residual nonequilibrium distribution of extra-high energy relic particles are obtained. The assumption about possibility of detection of "truly relic particles", which appeared at stage of early inflation, is put forward. Keywords: physics of the early universe, particle physics - cosmology connection, inflation, ultra high energy cosmic rays