Ward Identities for Scale and Special Conformal Transformations in Inflation

TL;DR

This paper derives general Ward identities for scale and special conformal transformations in single field inflation, valid to all orders in slow roll, with implications for observational cosmology.

Contribution

It provides a model-independent derivation of Ward identities for inflationary symmetries, including non-linear terms from spatial reparametrizations.

Findings

Ward identities are valid to all orders in slow roll.

Includes non-linear terms due to spatial reparametrizations.

Discusses potential observational consequences.

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.