On the thermodynamics of de Sitter spacetime and quasi-de Sitter spacetime

The de Sitter spacetime requires a source whose uniform energy density rho and pressure p are expressible as rho =-p=12 pi ²T²_H, where T_H=H/2 pi is the Hawking temperature and H is the Hubble constant. By applying the first law of thermodynamics the authors show that the total entropy vanishes identically for all observers, whatever the value of rho . These considerations are extended to eternal quasi-de Sitter spacetimes. A cosmological model of super-exponential inflation, for which H)0 and S_h(0, is on exactly the same footing, from the thermodynamical point of view, as the corresponding model of sub-exponential inflation, for which H(0 and S_h)0.