Establish the curved-space gravitational double copy

Establish a curved-space double-copy construction in which squaring Yang–Mills numerators yields Einstein-gravity correlators while preserving AdS cutting rules, Ward identities, factorization, and the appropriate curvature-dependent contact terms.

Background

The review explains that the upward dimension-shifting map from Yang–Mills theory to bi-adjoint scalar theory is established, whereas the downward map obtained by squaring numerators to reach Einstein gravity remains conjectural in the spectral construction. A naive four-point square fails to factorize correctly on partial-energy singularities because AdS graviton Ward identities require additional contact terms.

Resolving this problem would provide a curved-space replacement for the flat-space statement that gravity is the square of gauge theory, and would clarify how double-copy operations can be made compatible with bulk unitarity and cosmological wavefunction constraints.

References

The downward map, squaring the numerators to reach Einstein gravity in $AdS_{d-1}$, remains conjectural within this spectral construction; we return to what obstructs it below, and fixed-dimension Mellin-momentum constructions realize a four-point gravitational double copy by other means.

— Cosmological Correlators from Scattering Amplitudes: A Review  (2609.19252 - Albayrak et al., 16 Sep 2026) in Section 6.4, “Color–kinematics duality and the double copy”

While the Kerr--Schild structure is preserved, it would be interesting to explore whether these corrections admit a corresponding double-copy interpretation. We leave this question for future work.

— Braneworld tidal charge through the classical double copy  (2609.24521 - Cruz et al., 21 Sep 2026) in Section 3, Subsection 3.1, “Adding electromagnetic charge on the brane”

However, at four points gauge-to-gravity differential double copy for the four-stress-tensor correlator is not very well understood.

— Color-Kinematics Duality in the Cosmological Grassmannian  (2609.28639 - Bala et al., 23 Sep 2026) in Section 2, subsection “AdS Space Double Copy,” paragraph “Differential CK duality and double copy in AdS for four external scalar with gluon and graviton exchange”