On de Sitter radiation via quantum tunneling

We discuss why the tunneling picture does not necessarily lead to Hawking radiation from the de Sitter horizon. The experience with the condensed matter analogs of event horizon suggests that the de Sitter vacuum is stable against the Hawking radiation. On the other hand the detector immersed into the de Sitter background will detect the radiation which looks as thermal with the effective temperature twice larger than the Hawking temperature associated with the cosmological horizon.