Equation of State and Temperature of First Heavy Particles Arising in the Universe at the Grand Unification Scale,

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.