A de Sitter Farey Tail

          @misc{ pirsa_PIRSA:11060056,
            doi = {10.48660/11060056},
            url = {https://pirsa.org/11060056},
            author = {Maloney, Alexander},
            keywords = {Cosmology},
            language = {en},
            title = {A de Sitter Farey Tail},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {jun},
            note = {PIRSA:11060056 see, \url{https://pirsa.org}}
          }
          

Abstract

We compute the partition function of quantum Einstein gravity in three dimensional de Sitter space. The Euclidean path integral is formulated as a sum over geometries, including both perturbative loop and non-perturbative instanton corrections coming from geometries with non-trivial topology. These non-trivial geometries have a natural physical interpretation and lead to deviations from the standard thermal behaviour of the de Sitter horizon; this is the de Sitter analog of the celebrated "black hole Farey tail." Perturbative quantum corrections are computed to all orders in perturbation theory and the vacuum partition function, including all instanton and perturbative corrections, is shown to diverge in a way which can not be regulated using standard field theory techniques. Thus the Hartle-Hawking state is not normalizable.