requirement that $c_s \rightarrow 1$. To connect to the usual perturbation variables, one can make a gauge transformation to comoving gauge (see [@Cheung-consistency]) and find that $\zeta = - H \pi + {\cal O}(\pi^2)$.

We would like to emphasize again that for the inflationary background caused by canonical scalar fields, the interaction terms in the action of $\zeta$ are ${\cal O}(\epsilon^2)$ so that the interactions we are dealing with are different from those. Moreover, as is obvious from Eq (\[S\_SZ2010\]), in this regime the interaction terms are much simpler (and fewer) as compared to e.g. those in [@Maldacena-2003]. Thus, if we wish to try anything new e.g. loop corrections in cosmological perturbation theory and we want a regime which is realistic but which is also simple, this theory of large $\dot{\pi}^3$ interactions is the best possible choice [@SZ2010].

Given the action (Eq (\[S\_SZ2010\])), the Hamiltonian can be readily worked out and then one can use the in-in formalism (see [@PhysRevD.72.043514; @Contour_rotation] and references therein) to evaluate the two-point function at one-loop. In the rest of the present work, we shall focus on only the $\dot{\pi}^3$ term in the action given by Eq. (\[S\_SZ2010\]). This interaction term leads to two contributions 