Proton decay in de Sitter environment

The decay of proton in the de Sitter environment is governed by the temperature $T=H/\pi$, where $H$ is the Hubble parameter. This temperature is twice larger than the Gibbons-Hawking temperature $T_{\rm GH}=H/2\pi$. This demonstrates the physical difference of two processes. The temperature $T=H/\pi$ determines the proton decay rate in the local process which takes well inside the cosmological horizon. While the Gibbons-Hawking temperature can be related to the processes which involve the Hawking photons or other particles radiated from the cosmological horizon. The same temperature $T=H/\pi$ determines the radiation of electron-positron pairs by positron or by other object in the de Sitter environment. Creation of matter and its thermalization in the de Sitter heat bath leads to the energy exchange between matter and quantum vacuum and finally to the decay of the de Sitter state towards the Minkowski vacuum. The lesson for the Unruh effect is also discussed. One may expect the similar separation of effects governed by two different temperatures: the effects related to the Rindler horizon with the Unruh temperature $T_{\rm U}=a/2\pi$ and the local radiation with $T=a/\pi=2T_{\rm U}$.