General applicability of the GJMS and Q-curvature identification

Establish whether the cosmological response functions governing the logarithmic-gravity action reduce to the critical GJMS operator and Branson Q-curvature beyond no-boundary geometries with a real anti-de Sitter section satisfying the stated KSW criteria.

Background

For even spatial dimension and complex-conjugate bra–ket fillings admitting a real anti-de Sitter section, the paper identifies the cosmological response functions with the mathematical critical GJMS operator and Branson Q-curvature. The authors note that examples satisfying the relevant KSW criteria are not known beyond the sphere or deformed-sphere de Sitter fillings.

Consequently, it remains unresolved whether this identification applies to more general no-boundary geometries or fillings.

References

But the general applicability of \nref{PQmatheq} seems unclear if one believes the KSW criteria.

— Logarithmic gravity from a very slow roll limit of inflation  (2609.38052 - Cotler et al., 29 Sep 2026) in Section 4.2, “Relation to previous definitions,” paragraph beginning “However, a warning is that…”