Effective Temperature of the FRW Universe

Abstract In this paper, a new definition of temperature is proposed for the FRW(Friedmann–Robertson–Walker) universe, i.e., the effective temperature , where is the energy and is the entropy of the FRW universe. Based on this definition, the effective temperature is derived for the ‐dimensional FRW universe in Einstein gravity, Gauss–Bonnet gravity, and Lovelock gravity. For the 4‐dimensional FRW universe, the effective temperature is found to be , which is exactly the same form with the Hawking temperature of the Schwarzschild black hole. In higher‐dimensional FRW universe, the form of the effective temperature depends on the choices of the gravitational theories or the corresponding coupling constants. The free energy of the FRW universe in the three theories of gravity is also obtained.