Nonlinear gauge maps and the structure of Goldstone loops in canonical inflation

Abstract

We clarify the nonlinear relation between the spatially flat scalar and Goldstone descriptions of canonical single-field inflation. An exact clock map shows how potential interactions are reorganized into derivative Goldstone interactions. A change of slicing further connects their dilation symmetry to its comoving realization. We then study the Goldstone two-point function at one loop in the decoupling limit. Using identities derived from the general mode equation, we reveal how seemingly independent loop contributions combine and their non-boundary parts cancel once the associated counterterms are included. This reduction requires no explicit mode-function solution. The leading adiabatic long-mode response reduces to a total derivative in loop momentum, which requires an additional regularization prescription.