Holographic dual of quantum gravity in de Sitter space
In plain words
A universe with positive vacuum energy has no spatial boundary to hold an equivalent quantum theory. Where such a description lives and what it is are unknown.
Precise statement
Find a quantum system whose observables compute those of quantum gravity in asymptotically de Sitter space, for example a Euclidean CFT at future infinity (dS/CFT, Strominger 2001), a static-patch or horizon dual, or double-scaled SYK, reproducing at least the Gibbons-Hawking entropy and the tree-level wavefunction of the universe.
What would settle it
A quantum system with a derived dictionary reproducing the Gibbons-Hawking entropy and de Sitter graviton correlators at tree level.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Proposals based on double-scaled SYK (2022-2025) and on algebras of observables in the static patch (2022) are under debate.
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