Thermodynamics and Decay of de Sitter Vacuum

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, 𝐫→𝐫−𝑒𝐻𝑡𝐚, where H is the Hubble parameter. For 𝐻→0, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations 𝐫→𝐫−𝐚. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature 𝑇=𝐻/𝜋, which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature 𝑇=𝐻/𝜋 determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, 𝑆hor=4𝜋𝐾𝐴, where 𝐾=1/(16𝜋𝐺). This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the 𝑓(ℛ) gravity. In this thermodynamics, the Ricci scalar curvature ℛ and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling 𝐾=𝑑𝑓/𝑑ℛ. Such a connection takes place only in the 3+1 spacetime, where there is a special symmetry due to which the variables K and ℛ have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes.