Ahead of the hunt: leading small field inflationary potential models

We employ high accuracy computerized methods to check predictions of theoretical cosmological models against CMB observables specifically the spectral index n s its running n run and the running of the running n run run Our work is motivated by the recent developments in the hunt for primordial gravitational waves signal We therefore apply our work to small field models which present the possibility of generating appreciable GW signal while conforming to CMB observables Our research yields most probable inflation potential candidates among the 5th degree and 6th degree polynomial small field classes These candidates will be further challenged by new incoming data such as the anticipated BICEP3 Keck upcoming release We additionally find that for non vanishing n run the numerically extracted values of n s and n run deviate significantly from analytic projections We discuss the probable reasons for such deviations