An observer’s measure of de Sitter entropy

A bstract 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 $$ {e}^{-{S}_{\textrm{dS}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>dS</mml:mi> </mml:msub> </mml:mrow> </mml:msup> </mml:math> , 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.