QFT
In the literature: open
Entanglement-geometry relation outside anti-de Sitter space
In plain words
The rule that entanglement equals area of a surface in the bulk is established for spaces with negative vacuum energy. Whether a version holds in flat or expanding spacetimes is unknown.
Precise statement
Determine whether an analogue of the Ryu-Takayanagi formula $S = \mathrm{Area}/(4 G \hbar)$ for extremal surfaces holds in de Sitter or asymptotically flat quantum gravity, with an identified quantum system whose subregion entropies it computes (candidates include surfaces anchored at horizons or future infinity and timelike entanglement).
What would settle it
A derivation of an area formula from a defined dual system in de Sitter or flat space, checked against an independent entropy computation.