An Observer's Measure of De Sitter Entropy

The two-point correlation function of a massive field $⟨\chi (\tau )\chi (0)⟩$, measured along an observer’s worldline in de Sitter (dS), decays exponentially as $\tau \to \mathrm{\infty }$. Meanwhile, every dS observer is surrounded by a horizon and the holographic interpretation of the horizon entropy $S_{\mathrm{d}\mathrm{S}}$ 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 $e^{-S_{\mathrm{d}\mathrm{S}}}$, and which gives a constant contribution to $\mathrm{\mid }⟨\chi (\tau )\chi (0)⟩{\mathrm{\mid }}^2$. This constant might have the interpretation of the late-time average of $\mathrm{\mid }⟨\chi (\tau )\chi (0)⟩{\mathrm{\mid }}^2$ over all microscopic theories that have the same low-energy effective description.