  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.
