is true when $m^2 < 0$, but in that case, we can also write the same theory as ${\cal L} = - \frac{1}{2} (\partial \rho)^2 - \lambda v^2 \rho^2/6 - \lambda v \rho^3/6 - \lambda \rho^4/24$ (where $v = + (6 |m^2|/\lambda)^{1/2}$ and $\rho = \phi - v$) and looking at this Lagrangian, it may appear that we shall need more CTs for the $\rho^3$ term as well as to cancel the tadpole (i.e. divergent one-point function) it shall cause. In this case, the change of variables from $\phi$ to $\rho$ seems to suggest that we shall need more CTs while in reality, we do not. In contrast for the case we are dealing with, the process of taking $\eta \rightarrow 0$ limit suggests that we shall need fewer CTs, while in reality we do not.

Remarks on renormalization
--------------------------

In $\dot{\pi}^3$ theory, the field is $\pi$ while the various parameters appearing in the action are $\epsilon, H/M_{\rm Pl}$ and $c^3 M^4$. The parameter $c^3 M^4$ can be constrained from the observations of Primordial Non-Gaussianity in the CMB sky (and it has been constrained by the Planck collaboration [@Planck-2013-NG]). There also are (upper) limits on the values of $\epsilon$ and 