Frame-Independent Classification of Single-Field Inflationary Models

Seemingly unrelated models of inflation that originate from different physical setups yield, in some cases, identical predictions for the currently constrained inflationary observables. In order to classify the available models, we propose to express the slow-roll parameters and the relevant observables in terms of frame and reparametrization invariant quantities. The adopted invariant formalism makes manifest the redundancy that afflicts the current description of inflation dynamics and offers a straightforward way to identify classes of models which yield identical phenomenology. In this Letter, we offer a step-to-step recipe to recast every single field inflationary model in the proposed formalism, detailing also the procedure to compute inflationary observables in terms of frame and reparametrization invariant quantities. We hope that our results become the cornerstone of a new categorization of viable inflationary models and open the way to a deeper understanding of the inflation mechanism.