First Principle Study of Gravitational Pressure and Thermodynamics of FRW Universe

We make a first principle study of gravitational pressure in cosmic thermodynamics. The pressure is directly derived from the unified first law, in fact the Einstein field equation in spherically symmetric spacetime. By using this pressure, we obtain the thermodynamics for the FRW universe, especially presenting the gravitational equation of state for the FRW spacetime itself, i.e. $P=P(R_A, T)$ for the first time. Furthermore, we study the Joule-Thomson expansion as an application of the thermodynamic equation of state to find the cooling-heating property of the FRW universe. We demonstrate that there is an inversion temperature for a FRW universe if its enthalpy ${\cal H}$ is negative. These investigations shed insights on the evolution of our universe in view of thermodynamics.