to the two-point function only one of which is UV divergent (see [@SZ2010]). On canonical normalization, it becomes apparent that the $\dot{\pi}^3$ interaction is of mass dimension $+6$. In the action, a dimension six operator is expected to be accompanied with a factor of $1/{\Lambda_U}^2$, where $\Lambda_U$ is the unitarity bound  of the theory. This is what happens, on canonical normalization, $\pi_c \equiv \sqrt{- 2 \dot{H} M_{\rm Pl}^2 } ~ \pi$, and the coefficient of $\dot{\pi}_c^3$ operator turns out to be $$\frac{4}{3} \cdot \frac{c_3}{(2 \epsilon)^{3/2}} \cdot \frac{M^4}{H^3 M_{\rm Pl}^3} 
= \frac{4 c_3}{3} \cdot \frac{1}{\Lambda_U^2}$$ where $\Lambda_U$ is the energy scale at which this (non-renormalizable) theory becomes strongly coupled (i.e. the perturbative calculations are valid only at energy scales much smaller than this scale). We have, $$\frac{1}{{\Lambda_U}^2} = \frac{M^4}{(2 \epsilon)^{3/2} H^3 M_{\rm Pl}^3}$$ In correlators, it is expected that the (three-line) interaction vertex of $\dot{\pi}^3$ theory is always going to be accompanied with factors of the form $\frac{4 c_3}{3} \frac{H^2}{\Lambda_U^2}$ since $H$ is the energy scale of the inflationary experiment.  This suggests that for $\dot{\pi}^3$ theory, $$\label{gen_exp}
 \tilde{\cal G}_{\rm 1-loop} = k^3 (\tilde{\cal G}_{\rm tree})^2 \times \left( \frac{H^2}{\Lambda_U^2} \right)^2
 ({\rm factors}) \; .$$

Dimensional analysis and homogeneity of the background suggest 