Extend positive geometry to massive and spinning cosmological correlators

Extend cosmological polytopes, cosmohedra, optical polytopes, and related positive-geometric constructions to gravitons and massive exchanged fields so that massive collider signals and spinning correlators are represented geometrically.

Background

The review describes positive-geometric constructions that currently apply primarily to conformally coupled scalars, while separate developments address massless spinning fields. General masses and gravitons introduce additional analytic structures, including nonanalytic squeezed-limit behavior associated with cosmological-collider signals.

A successful extension would unify the geometric descriptions of wavefunction coefficients, unitarity, spinning structures, and massive-particle signatures, potentially connecting cosmohedra with Grassmannian descriptions of spinning correlators.

References

These constructions are young: the positive geometries are mostly limited to conformally coupled scalars, the Grassmannian to massless spinning fields, and extending either to general masses (gravitons, the cosmological collider) is open and inviting.

— Cosmological Correlators from Scattering Amplitudes: A Review  (2609.19252 - Albayrak et al., 16 Sep 2026) in Section 9.2, “Positive geometry: from polytopes to cosmohedra”