  We consider first heavy particles with masses $M\sim M_{GUT}$ which arise in
the Universe during phase transitions at the Grand Unification scale. Using
statistical mechanics approach we show that they behave like ideal quantum
degenerate Bose gas which has the temperature of the Hawking thermal radiation
due to presence of the de Sitter event horizon. The equation of state for both
scalar and gauge bosons is presented including the coupling constant at the
Grand Unification scale.
