Relational dynamics in axion-de Sitter universes

We study the evolution of codimension-one maximal volume and related geometric observables according to a pair of dynamical reference frames (i.e. observers) in asymptotically de Sitter universes in the presence of axion matter. This sources a Euclidean wormhole entangling the two universes, thereby changing the spacetime topology. The system is prepared in a two-copy Hartle-Hawking state by slicing a Euclidean wormhole. We derive the evolution of codimension-one observables anchored to the worldline reference frame in each universe. We investigate how the axion charge competes with the cosmological constant in the evolution of the observables. The maximal volume increases nearly exponentially for low axion charge, while it decreases to a vanishing value for the maximal axion charge allowed by de Sitter space.