Entanglement and factorization in axion-de Sitter universes (2312.08368v1)

Abstract: We study Renyi entropies and late-time bulk correlators between asymptotically de Sitter space universes connected through an Euclidean axion wormhole in arbitrary dimensions. We first establish the notion of entropy with respect to these observers within the background-independent approach to the algebra of operators. We then provide an explicit derivation of holographic Renyi entropies between the universes considering the dS/CFT correspondence. In the quantum mechanical description, the results can be recasted in terms of reduced density matrix where one of the asymptotically dS universes is traced out. Remarkably, our work shows that the throat of the Euclidean wormhole is associated with the entanglement between the universes. Later, we study correlators for heavy particles in the presence of an observer. We find that the Euclidean wormhole saddle allows for the late-time correlators with respect to observers located in the asymptotically dS universes to achieve a constant value at late times, while for the disconnected saddles do not contribute. The result is compatible with each of the asymptotically de Sitter universes being described by a finite-dimensional quantum dual theory. Lastly, we provide with an effective theory description of the dimensional reduction of these geometries in terms of dilaton-gravity theory with conformally coupled matter.