We explore thermodynamic contributions to the three-dimensional de Sitter horizon originating from metric and Chern-Simons gauge field fluctuations. In Euclidean signature these are computed by the partition function of gravity coupled to matter semi-classically expanded about the round three-sphere saddle. We investigate a corresponding Lorentzian picture — drawing inspiration from the topological entanglement entropy literature — in the form of an edge-mode theory residing at the de Sitter horizon. We extend the discussion to three-dimensional gravity with positive cosmological constant, viewed (semi-classically) as a complexified Chern-Simons theory. The putative gravitational edge-mode theory is a complexified version of the chiral Wess-Zumino-Witten model associated to the edge-modes of ordinary Chern-Simons theory. We introduce and solve a family of complexified Abelian Chern-Simons theories as a way to elucidate some of the more salient features of the gravitational edge-mode theories. We comment on the relation to the AdS4/CFT3 correspondence.
The two-point function of a free massive scalar field on a fixed background can be evaluated in the large mass limit by using a semiclassical geodesic approximation. In de Sitter space, however, this poses a puzzle. Certain spacelike separated points are not connected by real geodesics despite the corresponding two-point function in the Bunch-Davies state being non-vanishing. We resolve this puzzle by considering complex geodesics after analytically continuing to the sphere. We compute one-loop corrections to the correlator and discuss the implications of our results to de Sitter holography.
We investigate dilaton-gravity models whose solutions contain a large portion of the static patch of dS2. The thermodynamic properties of these theories are considered both in the presence of a finite Dirichlet wall, as well as for asymptotically near-AdS2 boundaries. We show that under certain circumstances such geometries, including those endowed with an asymptotically near-AdS2 boundary, can be locally and even globally thermodynamically stable within particular temperature regimes. First order phase transitions reminiscent of the Hawking-Page transition are discussed. For judiciously chosen models, the near-AdS2 boundary can be viewed as a completion of the stretched cosmological dS2 horizon. We speculate on candidate microphysical models.
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