Non-perturbative diffeomorphism invariance for doubled fields in Schwinger–Keldysh gravity

Establish a non-perturbative, diffeomorphism-invariant formulation of gravity within the Schwinger–Keldysh doubled-field formalism that enables a unitary-gauge derivation of the open Effective Field Theory of Inflation. Specifically, determine consistent rules for covariantizing indices in the presence of two metrics g^+_{\mu\nu} and g^-_{\mu\nu} (or mixed combinations) so that the ambiguity is resolved and the construction remains local, causal, and compatible with the diagonal symmetry action on the doubled fields.

Background

The paper develops an open Effective Field Theory of Inflation in the Schwinger–Keldysh framework, working primarily in the decoupling limit. While the standard EFToI may be derived in unitary gauge for a closed system, extending this derivation to an open system with doubled fields requires incorporating gravity in a manner consistent with diffeomorphism invariance.

The authors note that, beyond perturbative metric expansions, a fully diffeomorphism-invariant and non-perturbative organization of gravity in the doubled formalism is unclear. In particular, when both g^+_{\mu\nu} and g^-_{\mu\nu} are present, there appears to be an ambiguity in how to covariantize indices, suggesting the need for clear principles or constraints to fix the structure.