Ward Identities for Scale and Special Conformal Transformations in Inflation

TL;DR

This work derives general Ward identities for scale and special conformal transformations in single-field inflation, formulated in a gauge-fixed, wave-function-of-the-universe framework. The scale Ward identities reproduce Maldacena-type consistency relations and hold to all orders in slow-roll, while special conformal identities require a compensating spatial reparametrization, producing non-linear terms that still constrain inflationary correlators. The authors provide explicit checks for scalar and tensor two- and four-point functions and discuss late-time behaviour, including robustness to higher-derivative corrections and the presence of heavy fields. The results offer model-independent, symmetry-based constraints on inflationary observables, linking tensor-to-scalar ratios and non-Gaussianity, and clarifying when these Ward identities apply or fail (e.g., in multi-field scenarios).

Abstract

We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.