On the algebraic meaning of quantum gravity for closed Universes (2311.01952v1)

Abstract: Assuming the von Neumann algebra associated with a generic de Sitter observer is properly infinite (type III) we use Connes cocycle to identify the unique ( up to unitary equivalence) background independent dominant weight on an extended algebra formally including an external observer. The background independent algebra defined as the centralizer of this dominant weight is equipped with a semi finite trace. Quantum gravity effects, as well as an algebraic version of the no boundary Hartle Hawking partition function, can be defined by representing, classically different de Sitter closed Universes, as equivalence classes of finite projections in the background independent algebra. The associated generalized entropy is determined by the value of the semi finite trace on each equivalence class of finite projections.