cosmological correlations shall freeze at late times. Recently (see [@SZ_all_loops; @2013JHEP...02..151A]), it is claimed to be shown that this shall surely happen at all loops. The familiar primordial power spectrum $\Delta^2_{\zeta}(k)$ is defined by the Eq. $$\lim_{\eta \rightarrow 0^{-}} \langle \zeta(\eta,{\bf k}) \zeta(\eta,{\bf k}') \rangle = 
 \frac{2 \pi^2}{k^3}
~ \delta^3({\bf k} + {\bf k}') ~ \Delta^2_{\zeta}(k) \; ,$$ for slow roll inflation with a single (canonical) scalar field, the lowest order (i.e. tree level) contributions to power spectrum, assuming Bunch-Davies vacuum (in the limit $\eta \rightarrow 0^{-}$), is given by (the classic result) $$\label{eq:PS:free}
  \Delta^2_{\zeta}(k)|_{\rm tree} = \frac{1}{2 \epsilon(\eta_k)} \left(\frac{H(\eta_k)}{2 \pi M_{\rm Pl}} \right)^2 \; ,$$ where $\eta_k$ is the conformal time when the mode in question crosses Hubble radius (i.e. when $k = a H$). Notice that, on comparing with Eq (\[eq:def\_G\]), it becomes clear that for two-point function, $$\lim_{\eta \rightarrow 0} \tilde{\cal G}(\eta, {\bf k})|_{\rm tree} = 
  \frac{1}{4 \pi k^3} \Delta_{\zeta}^2 (k) = \frac{1}{32 \pi^3 k^3} \left( \frac{H^2}{\epsilon M_{\rm Pl}^2 } \right)\; .$$ Since the result in Eq (\[eq:PS:free\]) is obtained in linear theory, it corresponds to a free theory calculation. A well known fact is that Eq (\[eq:PS:free\]) implies that, the dimensionless Primordial Power spectrum is a 