A definite coordinate choice

We choose the scalar clock and the original inflaton-slice harmonic spatial coordinates described in BFHPR (equations (28)–(31)). We denote the latter by ${Y_{\Gamma }}^i$, and set

The modified spatial rods of equation (35) of that reference are not used. The two choices generally give different second-order observables. This distinction is part of the identification, not an approximation.

All calculations below use cosmic time and the action normalization in Section sec:theory. We do not import the reference's on-shell scalar formulas without converting their conventions.