Thermodynamic ensembles with cosmological horizons

Understand

The entropy of a de Sitter horizon was derived long ago by Gibbons and Hawking via a gravitational partition function.

• Since there is no boundary at which to define the temperature or energy of the ensemble, the statistical foundation of their approach has remained obscure.
• To place the statistical ensemble on a firm footing we introduce an artificial "York boundary", with either canonical or microcanonical boundary conditions, as has been done previously for black hole ensembles.
• The partition function and the density of states are expressed as integrals over paths in the constrained, spherically reduced phase space of pure 3+1 dimensional gravity with a positive cosmological constant.