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As distinct from the black hole physics, the de Sitter thermodynamics is notdetermined by the cosmological horizon, the effective temperature differs fromthe Hawking temperature. In particular, the atom in the de Sitter universeexperiences thermal activation corresponding to the local temperature, which istwice larger than the Hawking temperature, $T_{\rm loc}=2T_{\rm Hawking}$. Thesame double Hawking temperature describes the decay of massive scalar field inthe de Sitter universe. The reason, why the local temperature is exactly twicethe Hawking temperature, follows from the geometry of the de Sitter spacetime.The weakening of the role of the cosmological horizon in de Sitter universe isconfirmed by considering Hawking radiation. We discuss the difference betweenthe radiation of particles in the de Sitter spacetime and the Schwinger paircreation in the electric field. We use the stationary Painleve-Gullstrandmetric for the de Sitter spacetime, where the particles are created by Hawkingradiation from the cosmological horizon, and time independent gauge for theelectric field. In these stationary frames the Hamiltonians and the energyspectra of massive particles look rather similar. However, the final resultsare essentially different. In case of Schwinger pair production the numberdensity of the created pairs grows with time, while in the de Sitter vacuum thenumber density of the created pairs is finite. The latter suggests that Hawkingradiation from the cosmological horizon does not lead to instability of the deSitter vacuum. The other mechanisms of instability are required for thedynamical solution of the cosmological constant problem. We consider thepossible role of the local temperature $T_{\rm loc}=2T_{\rm H}$ in the decay ofthe de Sitter space-time due to the energy exchange between the vacuum energyand relativistic matter with this temperature.

Double Hawking temperature in de Sitter Universe and cosmological constant problem