Information, Geometry, and Physics Seminar

We study algebras of observables for semiclassical quantum gravity in cosmological backgrounds, focusing on two key examples: slow-roll inflation and evaporating Schwarzschild-de Sitter black holes. In both cases, we demonstrate the existence of a nontrivial algebra of diffeomorphism-invariant observables ​**without** the introduction of an explicit clock system or the presence of any asymptotic gravitational charges. Instead, the rolling inflaton field and the evaporating black hole act as physical clocks that allow a definition of gauge-invariant observables at G = 0. The resulting algebras are both Type II_\infty factors. For appropriate states, we establish a connection between the Type II entropy of these algebras and generalized entropies. Our work extends previous results on Type II gravitational algebras and highlights the crucial role of out-of-equilibrium dynamics when defining gauge-invariant observables in semiclassical canonically quantised gravity.