de Sitter and Cosmological Holography
Cosmological holography asks what boundary or observer data can describe an expanding spacetime. Late-time wavefunctions, static-patch algebras, horizon entropy, and lower-dimensional models answer different parts of that question; this chapter compares their observables and limitations.
Enter this chapter
Section titled “Enter this chapter”Begin with de Sitter and Cosmological Holography to identify the object a proposed dictionary encodes.
Helpful background. de Sitter Infrared Regimes: States, Observables, Gauges, and Limits and In-In Cosmological Correlators supply de Sitter state choices and normalized cosmological expectation values.
Topics
Section titled “Topics”- de Sitter and Cosmological Holography — Classifies proposals by boundary object, observer, and quantum state.
- de Sitter Observables, States, and Horizon Patches — Distinguishes global data from quantities accessible in one horizon patch.
- Late-Time Wavefunctions and Boundary Data — Separates local phases from nonlocal wavefunction coefficients.
- dS/CFT Dictionaries and Analytic Continuation — Tracks phases and boundary conditions under AdS-to-dS continuation.
- Wavefunction Coefficients versus In-In Correlators — Derives normalized expectation values from wavefunction data.
- Cosmological Bootstrap as Holographic Input — Uses symmetry, singularities, and factorization to constrain bulk interactions.
- Static-Patch Algebras and Observer Dependence — Explains how clocks and gravitational constraints affect the accessible algebra.
- de Sitter Entropy and Finite-Hilbert-Space Proposals — Tests when finite entropy can be interpreted as a finite state count.
- Higher-Spin de Sitter Examples — Studies explicit continued higher-spin models and their probability limitations.
- Matrix and Lower-Dimensional de Sitter Models — Identifies the contours and observables of solvable low-dimensional models.
- de Sitter Holography: Dictionary Completeness, Obstructions, and Status — Compares the ingredients supplied by each proposed dictionary.
How the ideas fit together
Section titled “How the ideas fit together”A late-time wavefunction is an amplitude for boundary field configurations. Its coefficients constrain bulk dynamics, but expectation values require multiplying by the complex conjugate, normalizing, and integrating over those configurations. An AdS-to-dS continuation must therefore track phases and state preparation before any probability interpretation Harlow and Stanford 2011, §§ 3–4. A static observer asks a further question: which operations lie in the accessible algebra? Agreement of late-time coefficients cannot supply that algebra, just as a finite entropy by itself cannot determine an exact Hilbert-space dimension.
Claim-domain comparison
Section titled “Claim-domain comparison”Compare the assumptions and strongest supported conclusion for each case.
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| Claim object | State, ensemble, and conventions | Approximation, status, and evidence timing | Uncertainty and counterevidence | Falsifier | Failure condition | Licensed conclusion |
|---|---|---|---|---|---|---|
| late-time wavefunction | Declare state, boundary data, and phase convention; use the volume conventions unless the page states a local replacement. | Model-specific calculation or conditional result. Control chain: de Sitter state and observer patch → wavefunction or in-in observable → analytic continuation and dictionary → entropy and static-patch tests → proposal status. Sources are cited on the destination page; literature checked through 10 August 2026. | Track omitted corrections, alternate branches, and competing definitions. A failed “Ward and analytic-continuation check” check is counterevidence to the promoted claim. | The coefficient violates the applicable isometry Ward identity or the stated continuation prescription for the chosen state and branch. | Interpreting complex wavefunction coefficients as ordinary Euclidean CFT probabilities. | wavefunction coefficients |
| in-in correlator | Declare closed-time contour and operator ordering; use the volume conventions unless the page states a local replacement. | Model-specific calculation or conditional result. Control chain: de Sitter state and observer patch → wavefunction or in-in observable → analytic continuation and dictionary → entropy and static-patch tests → proposal status. Sources are cited on the destination page; literature checked through 10 August 2026. | Track omitted corrections, alternate branches, and competing definitions. A failed “reality and cutting checks” check is counterevidence to the promoted claim. | A Hermitian observable acquires a nonreal expectation value, or the required closed-time-contour cutting relation fails after all terms are included. | Identifying an in-in expectation value with a wavefunction coefficient. | cosmological expectation value |
| static-patch proposal | Declare observer algebra and horizon state; use the volume conventions unless the page states a local replacement. | Proposal or conditional construction. Control chain: de Sitter state and observer patch → wavefunction or in-in observable → analytic continuation and dictionary → entropy and static-patch tests → proposal status. Sources are cited on the destination page; literature checked through 10 August 2026. | Track omitted corrections, alternate branches, and competing definitions. A failed “entropy and finite-system consistency” check is counterevidence to the promoted claim. | The proposed observer state is not positive, or fails the thermal or entropy relation actually claimed for its specified algebra. | Promoting one observer description to complete global de Sitter holography. | a model-dependent observer description |
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Where to go next
Section titled “Where to go next”Continue to Flat-Space, BMS, and Celestial Holography to compare boundary proposals based on scattering and null infinity.