de Sitter and Cosmological Holography

“de Sitter holography” names several proposals with different boundary objects: a late-time wavefunction represented by Euclidean data, an algebra accessible to a static observer, horizon or stretched-screen degrees of freedom, and lower-dimensional matrix or dilaton models. They do not supply interchangeable answers. Every claim must specify the state, patch, observer, boundary condition, inner product, reconstruction target, and perturbative or nonperturbative domain.

Required background. Wavefunction and Correlator Object Dictionary distinguishes the cosmological objects; Holographic Duality: Claims, Dictionaries, and Regimes supplies the claim standard.

Helpful background. de Sitter Infrared Regimes: States, Observables, Gauges, and Limits controls the QFT domain; Dictionary Completeness and Global Data identifies information a full duality would have to contain.

Three inequivalent proposal classes

In global coordinates de Sitter has spacelike conformal boundaries $\mathcal I^-$ and $\mathcal I^+$. The dS/CFT proposal relates the late-time Hartle–Hawking/Bunch–Davies wavefunction to a Euclidean generating functional,

$$\Psi_{\mathrm{BD}}[\varphi_+] \stackrel{?}{=}Z_{\mathrm{Euc}}[\varphi_+],$$

with parameters often obtained by analytic continuation from Euclidean AdS Strominger 2001, §§ 2–4. The encoded object is a functional of future-boundary data. It is not automatically a Lorentzian Hilbert space, a positive inner product, or a finite-time observable algebra.

A static-patch proposal begins instead with one observer’s causal diamond and cosmological horizon. In semiclassical gravity, worldline-dressed observables form an algebra with a thermal/KMS state. The recent crossed-product construction yields a type-II$_1$ algebra in a controlled semiclassical setting and an entropy matching generalized entropy up to an additive constant Chandrasekaran et al. 2023, §§ 2–5. This is an algebraic statement for a patch; it does not reconstruct global $\mathcal I^+$ data or prove a finite exact Hilbert space.

Lower-dimensional dS JT and matrix proposals define specific path integrals, genus expansions, or scattering-like boundary amplitudes. Their contours and topology weights are part of the theory. Solvability can reveal factorization and completion problems, but dimensions, degrees of freedom, and observables differ from four-dimensional de Sitter.

First application: classify before comparing

Consider the following three representative claims.

Late-time dS/CFT. The object is $\Psi[\varphi_+]$ or its coefficient functions at $\mathcal I^+$. The usual state is selected by a Euclidean/Bunch–Davies contour. Quantitative checks include free-field kernels, analytic continuation of AdS Witten diagrams, conformal Ward identities, and selected higher-spin examples. A positive Euclidean inner product and a complete finite-time bulk reconstruction map are generally absent.

Static-patch algebra. The object is an observer- and clock-dressed von Neumann algebra with a state. Quantitative checks include detector KMS response and generalized-entropy differences. It addresses finite-time accessible observables, but only within a chosen patch and semiclassical dressing; the horizon complement and global state are not encoded by assumption.

dS JT/matrix model. The object is a specified lower-dimensional gravitational path integral or boundary amplitude, frequently organized by a genus expansion and a matrix-integral continuation. Quantitative checks include exact moduli integrals and resummation properties Cotler and Jensen 2024, §§ 2–5. Whether the object is a fixed theory, an ensemble average, or a formal analytic continuation depends on its contour and completion.

These proposals can illuminate one another without sharing an observable. A late-time coefficient is not an entry of a static-patch density matrix, and a two-dimensional genus expansion is not evidence for a four-dimensional boundary CFT.

Regime and completeness limits

Semiclassical de Sitter requires $G_NH^{d-1}\ll1$ and curvature $H^2$ below any string or higher-derivative scale. A top-down model must additionally control $g_s$, $\alpha'H^2$, Kaluza–Klein modes, moduli, and metastable decay. Late-time perturbation theory can fail through infrared or secular effects even when curvature is small. No proposal may inherit AdS unitarity, factorization, or Hamiltonian evolution merely by continuation.

Adversarial control: request one finite-time observable

Ask each proposal for the transition rate of a geodesic Unruh–DeWitt detector operated for a finite interval in one static patch, with switching function and Bunch–Davies state fixed. Static-patch QFT defines it directly. A late-time dS/CFT proposal must supply an inner product and reconstruction map; a wavefunction coefficient alone is not the answer. A dS JT model answers only its lower-dimensional analogue. Record an absent map as absent rather than translating by terminology.

The evidence ceiling is a collection of precise partial dictionaries and model calculations. None presently supplies, across generic de Sitter quantum gravity, a common boundary Hilbert space, normalized finite-time observables, unitary evolution, reconstruction, and nonperturbative completion. The individual leaves develop each object; changing comparative confidence belongs to dated research review.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Chandrasekaran, V., Longo, R., Penington, G., and Witten, E. (2023). “An Algebra of Observables for de Sitter Space.” Journal of High Energy Physics 2023(2), 082. DOI.
• Cotler, J., and Jensen, K. (2024). “Non-Perturbative de Sitter Jackiw–Teitelboim Gravity.” Journal of High Energy Physics 2024(12), 016. DOI.
• Strominger, A. (2001). “The dS/CFT Correspondence.” Journal of High Energy Physics 2001(10), 034. DOI.