An observer’s measure of de Sitter entropy

The two-point correlation function of a massive field ⟨χ(τ)χ(0)⟩, measured along an observer’s worldline in de Sitter (dS), decays exponentially as τ → ∞. Meanwhile, every dS observer is surrounded by a horizon and the holographic interpretation of the horizon entropy S_dS suggests that the correlation function should stop decaying, and start behaving erratically at late times. We find evidence for this expectation in Jackiw-Teitelboim gravity by finding a topologically nontrivial saddle, which is suppressed by $e^{-S_{\mathrm{dS}}}$ \( {e}^{-{S}_{\textrm{dS}}} \) , and which gives a constant contribution to | ⟨χ(τ)χ(0)⟩ |². This constant might have the interpretation of the late-time average of | ⟨χ(τ)χ(0)⟩ |² over all microscopic theories that have the same low-energy effective description.