QFT
In the literature: open
Positive geometry for de Sitter correlators of massless fields
In plain words
A geometric shape, the cosmological polytope, gives the quantum state of the early universe for a simple toy field. Extending it to the fields that matter, such as massless particles and gravitons in an expanding universe, is open.
Precise statement
The cosmological polytope (Arkani-Hamed, Benincasa, Postnikov, 2017) gives wavefunction coefficients of conformally coupled scalars with polynomial interactions in flat space and FRW backgrounds as canonical forms. Find a positive geometry whose canonical form gives tree-level wavefunction coefficients or in-in correlators of massless minimally coupled scalars or gravitons in de Sitter space.
What would settle it
An explicit geometry reproducing the known four-point graviton or massless-scalar de Sitter wavefunction coefficients.