unfamiliar divergences, and still deal with a realistic model of cosmological perturbations which has simple interactions, we work with the theory of large $\dot{\pi}^3$ interactions [@SZ2010].  The Effective Field Theory (EFT) [@EFT2008] of inflation provides the most general framework for systematically studying the dynamics of fluctuations around an inflationary background solution. The action of the theory of fluctuations can be expanded in powers of the relevant fluctuation field (and also in powers of the slow-roll parameters such as the Hubble flow functions). The theory is first formulated in unitary slicing of the perturbed spacetime in which $\delta \phi$ vanishes (and all the dynamics lies in the metric) and then general covariance is restored by introducing the Stueckelberg field (denoted by $\pi$ in the following). It turns out that if one chooses to ignore ${\cal O}(\epsilon^2)$ terms in the action (which also corresponds to the interaction terms which give rise to primordial non-Gaussianity for a canonical scalar field, see [@Maldacena-2003]), and one chooses to fix the sound speed of fluctuations to unity (i.e. we wish to only consider the cases in which $c_s \rightarrow 1$), [^1] the leading order interactions for the Stueckelberg field shall be captured by terms of the 