An exact holographic dual of de Sitter space: existence, identity, and consistency

De Sitter space, the maximally symmetric solution of general relativity with positive cosmological constant and the asymptotic geometry of our accelerating universe, has no established holographic dual. The AdS/CFT correspondence provides exact, non-perturbative duals for negatively curved spacetimes, but every de Sitter proposal to date - dS/CFT, the dS/dS correspondence with $T\bar T$-deformed wall theories, static-patch screen holography with monolayer/bilayer entropy prescriptions, half-de Sitter, double-scaled Sachdev–Ye–Kitaev (SYK) models (the SYK model being an exactly solvable quantum-mechanical model of randomly coupled fermions), and Lorentzian-torus constructions - remains a proposal or a semiclassical/large-N match. The problem is to construct, or rigorously rule out, a precisely defined dual theory reproducing de Sitter quantum gravity, including its horizon entropy, late-time correlators, and backreaction, and thereby bearing on the open structural puzzles: semiclassical mode instabilities, the integrability versus chaoticity of $T\bar T+\Lambda_2$-deformed duals, and the missing replica derivation of the bilayer generalized-entropy prescription.

Background

De Sitter space (dS) is the maximally symmetric solution of Einstein's equations with positive cosmological constant $\Lambda$; our universe, whose expansion is accelerating, approaches de Sitter in the far future. Any observer in de Sitter space is surrounded by a cosmological horizon with a finite Gibbons–Hawking entropy $S_{\rm dS} = A/4G\hbar$ proportional to the horizon area - the cosmological analogue of Bekenstein–Hawking black-hole entropy. The holographic principle asserts that a quantum theory of gravity in a spacetime volume can be fully encoded in a non-gravitational theory with fewer dimensions living on a boundary; it is realized exactly in the AdS/CFT correspondence, where quantum gravity on anti-de Sitter space (constant negative curvature) is dual to an ordinary conformal field theory (CFT, a scale-invariant quantum field theory). Whether an analogous exact dual exists for de Sitter space - and hence for quantum gravity in a cosmological spacetime like ours - is a long-standing open problem of quantum gravity.

The candidate proposals delimit what is known. In the dS/CFT correspondence (Strominger, 2001), quantum gravity on $\mathrm{dS}_{d+1}$ would be dual to a Euclidean CFT on the sphere at future infinity; unlike AdS/CFT, no controlled instance is known, and basic dictionary questions - how bulk wave functions map to boundary operators - remain unresolved (Harlow and Stanford, 2011). In the dS/dS correspondence (Alishahiha, Karch, Silverstein, and Tong, 2004), de Sitter space is viewed as two de Sitter patches of one lower dimension separated by a wall, with a tentative dual of two CFTs at different temperatures coupled along an interface; at large $N$ (the limit of many degrees of freedom) the wall theory is described by a $T\bar T$-deformed CFT (Gorbenko, Silverstein, and Torroba, 2019), where $T\bar T$ denotes the irrelevant deformation of a two-dimensional CFT by the determinant of its own stress tensor - a deformation that places the theory at a finite radial cutoff; adding the further $\Lambda_2$ term, a constant deformation whose strength is fixed by the bulk cosmological constant, allows the deformed theory to live on the stretched cosmological horizon of three-dimensional de Sitter (a surface just outside the horizon). The exact, non-perturbatively defined dual theory in this framework has not been identified, and even its basic character is unknown: entanglement-entropy scaling suggests the $T\bar T+\Lambda_2$-deformed dual is chaotic rather than integrable (Geng, 2020), a question still open. A third program encodes the static patch - the causal diamond of a single de Sitter observer - on holographic screens at the cosmological horizon, with competing 'monolayer' and 'bilayer' prescriptions for holographic entanglement entropy; the bilayer, two-screen prescription is argued to be self-consistent (Franken et al., 2023) and has been extended to de Sitter geometries containing bubbles of smaller or vanishing cosmological constant (Irakleous, Rondeau, and Toumbas, 2025), but the covariant bilayer generalized-entropy prescription still lacks a derivation from a bulk replica path integral - an entanglement-entropy computation that glues together copies of the spacetime along a cut - of the kind that grounds the Ryu–Takayanagi formula, the AdS/CFT rule equating boundary entanglement entropy with areas of bulk extremal surfaces. Separately, semiclassical de Sitter is itself subtle: computing the expectation value of the stress tensor of a strongly coupled quantum field theory by holographic means and feeding it into the semiclassical Einstein equations, one finds de Sitter is mode-unstable below a critical Hubble scale (Chesler and Loeb, 2020; extended to other dimensions by Ishibashi, Maeda, and Okamura, 2026) - a constraint any candidate dual must eventually explain.

Here 'exact' is meant in the AdS/CFT sense: a precisely specified boundary theory defined non-perturbatively (not merely an effective or large-$N$ description), a complete dictionary, and demonstrated agreement with bulk quantum gravity on observables beyond what any semiclassical prescription could fit. By this standard no de Sitter dual is established, and whether the obstruction is technical or fundamental is not known.

Problem Statement

Does there exist an exact holographic dual of de Sitter quantum gravity, and if so, what is it?

Construct, or rule out, a precisely defined holographic dual description of quantum gravity on de Sitter space - in any dimension, or in an explicitly specified class of de Sitter spacetimes that includes at least one fully worked example. A construction must supply three jointly necessary components of one scientific objective: (1) the dual theory itself, with its degrees of freedom and non-perturbative definition (Hamiltonian, path integral, or complete axioms), not merely an effective or large-$N$ semiclassical description; (2) a dictionary mapping bulk de Sitter observables to dual quantities, including at minimum the late-time (future-boundary) correlation functions of matter fields, the Gibbons–Hawking horizon entropy with its leading quantum corrections, and the response to bulk backreaction; and (3) demonstrated, verifiable agreement between dual and bulk computations in a controlled regime, including at least one quantity genuinely beyond semiclassical gravity, together with precise consistency with the known structural constraints: the dimension-dependent mode-stability structure of semiclassical de Sitter and, where the construction invokes the relevant framework, the monolayer/bilayer entropy prescriptions and the integrability or chaoticity of $T\bar T$-type deformed duals.

A no-go answer is equally admissible: a proof, from explicitly stated assumptions, that no boundary theory satisfying the three requirements above can holographically reproduce de Sitter quantum gravity. A construction may be given for an explicitly specified class of de Sitter spacetimes - for example, three-dimensional de Sitter, a single static patch, or a subsector - provided the three requirements above are met within that class and the dual theory there has a complete, non-perturbative definition.

References

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