Abstract

Multiple lines of evidence suggest that the Hilbert space of an isolated de Sitter (dS) universe is one dimensional, but can appear larger when probed by a gravitating observer. To test this idea, we compute the von Neumann entropy of a field theory in a two-dimensional dS universe which is entangled in a thermal-like state with the same field theory on a disjoint, asymptotically anti-de Sitter (AdS) black hole.   We show that the entanglement entropy vanishes if the dS cosmological horizon is smaller than the AdS black hole horizon, but that non-perturbative contributions of wormholes in the gravitational path integral imply that the entanglement entropy is finite when the dS horizon is larger than the AdS horizon. Thus, the dS Hilbert space is effectively nontrivial only when the cosmological horizon is larger than the horizon of the entangled AdS black hole, which we can regard as a gravitating ``observer’’. In this sense, our result is a non-perturbative generalization  of the recent perturbative argument that the algebra of observables on the de Sitter static patch becomes nontrivial in the presence of an observer.