  As distinct from the black hole physics, the de Sitter thermodynamics is not
determined by the cosmological horizon, the effective temperature differs from
the Hawking temperature. In particular, the atom in the de Sitter universe
experiences thermal activation corresponding to the local temperature, which is
twice larger than the Hawking temperature, $T_{\rm loc}=2T_{\rm Hawking}$. The
same double Hawking temperature describes the decay of massive scalar field in
the de Sitter universe. The reason, why the local temperature is exactly twice
the Hawking temperature, follows from the geometry of the de Sitter spacetime.
The weakening of the role of the cosmological horizon in de Sitter universe is
confirmed by considering Hawking radiation. We discuss the difference between
the radiation of particles in the de Sitter spacetime and the Schwinger pair
creation in the electric field. We use the stationary Painleve-Gullstrand
metric for the de Sitter spacetime, where the particles are created by Hawking
radiation from the cosmological horizon, and time independent gauge for the
electric field. In these stationary frames the Hamiltonians and the energy
spectra of massive particles look rather similar. However, the final results
are essentially different. In case of Schwinger pair production the number
density of the created pairs grows with time, while in the de Sitter vacuum the
number density of the created pairs is finite. The latter suggests that Hawking
radiation from the cosmological horizon does not lead to instability of the de
Sitter vacuum. The other mechanisms of instability are required for the
dynamical solution of the cosmological constant problem. We consider the
possible role of the local temperature $T_{\rm loc}=2T_{\rm H}$ in the decay of
the de Sitter space-time due to the energy exchange between the vacuum energy
and relativistic matter with this temperature.
