Equation of State for Particles Arising at the Universe at Grand Unification Energies

First postinflationary stage of the Universe evolution is considered in more detail. It is shown that heavy particles with mass $M_{H}\sim M_{GUT}$ arising at the Universe at phase transitions at Grand Unification Energies behave like ideal quantum degenerate Bose gas. The equation of state for both scalar and gauge bosons is presented including the coupling constant and vacuum expectation value at $E_{GUT}$. One possible way is proposed to connect cosmological observational data with parameters of Grand Unified Theories.