arXiv2023
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 gravity to do so and investigate timelike boundaries in these theories, with an emphasis on the stretched horizon holographic picture. Given the success of AdS/CFT, one might try to embed de Sitter inside anti-de Sitter and describe the expanding region from the boundary. In two dimensions, such geometries exist and, by studying them in the presence of a timelike boundary, we find thermally stable solutions. We thus propose a dual matrix model that should describe this geometry, including the expanding region. One way to test this duality would be to compare bulk and boundary correlators. However, for de Sitter this poses a puzzle: in the saddle point approximation two-point functions are given by a sum over geodesics. Such correlation functions exist for any two arbitrary points in de Sitter, but geodesics do not. This is resolved by including complex saddles that appear upon Wick rotating from the sphere. Additionally, one can use the 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 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 a comparable Abelian theory that leads to an entropy with an entanglement character. Finally, we summarise some new results on edge-mode theories arising from general boundary conditions.