Abstract
This thesis explores the thermodynamics of the cosmological horizon, aiming to make progress towards a better understanding of the microscopic nature of its entropy. We utilise the constrained nature of low-dimensional theories of gravity to do so and investigate timelike boundaries in these theories, with an emphasis on the stretched horizon holographic picture. Throughout, we make use of the Euclidean continuation of de Sitter to the sphere.Given the success of the AdS/CFT correspondence, one might attempt to embed a piece of de Sitter inside an anti-de Sitter geometry, and then describe the expanding region from the AdS boundary. In two dimensions, there exist dilaton potentials that give rise to such geometries and, by studying this problem in the presence of a timelike boundary, we demon-strate how to stabilise such solutions against thermal fluctuations. We then propose a dual matrix model living at the AdS boundary that should describe the interior spacetime, includ-ing the expanding region. Having proposed such a duality, a key method for testing it would be to compare correlation functions in the bulk and boundary. However, for de Sitter this poses a puzzle: in the saddle point approximation two-point functions can be calculated as a weighted sum over geodesic lengths. Such correlation functions are known to exist for any two points in de Sitter, but geodesics do not exist between arbitrary points. The puzzle is resolved by including complex length saddles that appear upon analytic continuation from the sphere.
Additionally, one can use the semi-classical relationship between three-dimensional gravity and Chern-Simons theory to explore thermodynamic contributions to the de Sitter horizon.
The Euclidean gravitational path integral provides the exact, all-loop quantum corrected de Sitter entropy. To better understand the microscopic origin of this entropy, one hopes to find an analogous Lorentzian calculation that produces this result. This takes the form of an edge-mode theory living close to the cosmological horizon with a complexified gauge group, leading to an unbounded spectrum. To make progress, we study an analogous Abelian theory and see that the there is an entanglement character to the entropy of the horizon. Finally, we summarise some new results on edge-mode theories arising from general boundary conditions.
| Date of Award | 1 Nov 2023 |
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| Original language | English |
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| Supervisor | Dionysios Anninos (Supervisor) & Christopher Herzog (Supervisor) |