Density matrix realizing maximal empty-de-Sitter entropy

Construct a density matrix that realizes the entropy of empty de Sitter space if empty de Sitter is the maximum-entropy state.

Background

The paper considers the conjecture that the total entropy consists of the de Sitter horizon entropy plus the entropy of matter and radiation visible to an observer. As matter leaves the horizon, the visible entropy decreases while the horizon contribution increases, suggesting that empty de Sitter space could be a maximum-entropy state.

The unresolved issue is which density matrix, in an appropriate gravitationally dressed or observer-dependent algebra, realizes that maximal entropy. This question is complicated by the failure of Hilbert-space factorization and the type-III nature of local quantum-field-theory algebras.