On thermal radiation of de Sitter space in the semiclassical Jackiw–Teitelboim model

In general, the Gibbons–Hawking temperature based on the Euclidean functional approach shows that de Sitter space in the Bunch–Davies vacuum is globally thermal. In the exactly soluble semiclassical Jackiw–Teitelboim model, we investigate thermal property of de Sitter space by taking into account the quantum back reaction of the geometry. The proper temperature of de Sitter space in the Bunch–Davies vacuum is found to vanish. In case of a certain quantum state breaking the de Sitter symmetry, de Sitter space can be made thermally exited; however, in this case the dilaton singularity cannot be avoided. Consequently, in the Jackiw–Teitelboim model the proper temperature of de Sitter space in the Bunch–Davies vacuum turns out to be zero and the Bunch–Davies vacuum is found to be the only physical vacuum without any naked singularities.