Generalized Entanglement Capacity of de Sitter Space

TL;DR

This paper explores the thermodynamic properties of de Sitter space horizons, extending the concept of generalized entropy to a generalized heat capacity, and suggests a finite-dimensional quantum gravity interpretation.

Contribution

It introduces a generalized heat capacity for de Sitter horizons and links it to the Bekenstein-Hawking entropy, extending thermodynamic concepts in quantum gravity.

Findings

Generalized heat capacity of de Sitter horizon equals its entropy.

Thermodynamic quantities exhibit cutoff sensitivities similar to conformal field theories.

De Sitter space can be viewed as a finite-dimensional quantum state.

Abstract

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of dS. The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggests it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain.