An Observer's Measure of De Sitter Entropy

TL;DR

The paper investigates how an observer measuring a massive scalar correlator in de Sitter spacetime might escape the naive exponential decay predicted by effective field theory due to horizon entropy. By employing Jackiw-Teitelboim gravity in a dynamical-observer setup, it identifies a topologically nontrivial wormhole saddle that couples the ket and bra sectors and contributes a constant term to the late-time |<χ(τ)χ(0)>|^2$, suppressed only by e^{-S_dS}. This nonperturbative effect offers a potential interpretation as the late-time average over microstates consistent with the same low-energy description, hinting at holographic structure in de Sitter space. The work further analyzes backreaction, showing how disk and wormhole saddles can coexist and how large backreaction can alter timing and stability of these saddles, raising questions about the existence and nature of a dS holographic dual and the role of higher-genus contributions. Overall, it provides a concrete gravitational mechanism for non-decaying late-time correlations and opens avenues for understanding dS information content and Page-like transitions.

Abstract

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

Figures (4)

• Figure 1: The Hartle-Hawking prescription for the wavefunction. With this prescription, any observer maximally extends into two (the red curve).
• Figure 2: The Lorentzian parts of the geometry that corresponds to the contour \ref{['rho_contour']}, embedded in the Penrose diagram of the global cover of dS$_2$. The dotted lines within each wedge are identified. The conical singularities are avoided by contour deformations at $0$,$i\pi$ and $2i\pi$.
• Figure 3: Analytic continuation of the geodesics in \ref{['trumpet_geod']}, on the global cover of the expanding cones of figure \ref{['fig:cones']}. $y=$ constant geodesics (blue) connect points on the two sides: $1\to 1'$ and $2\to 2'$. Their length is Euclidean, $2i\pi$. This is consistent with the expectation that the accumulated phase during the Lorentzian propagation should cancel between the $|{\rm ket}\rangle$ and the $\langle {\rm bra}|$. Each red curve in \ref{['trumpet_geod']} gives the pair of observers either on the $|{\rm ket}\rangle$ or $\langle {\rm bra}|$.
• Figure 4: Double trumpet geometry, including the matter back-reaction on the dilaton.