Counterterms in cosmological perturbation theory {#sec:cosmo_pert}
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In inflationary cosmological perturbation theory, the most relevant correlator is the late time limit of $n-$point function of (Heiseberg picture) comoving curvature perturbation, $\zeta$ on a constant time hyper-surface $$\lim_{\eta \rightarrow 0^-} 
\langle \Omega | \zeta(\eta,{\bf x}_1) \zeta(\eta,{\bf x}_2) \cdots \zeta(\eta,{\bf x}_n) | \Omega \rangle \; .$$ Homogeneity of the inflationary background implies that all such correlators shall be invariant under translations in space at a fixed time, which implies that the Fourier transform of the above correlator shall be of the form $$\label{eq:def_G}
 F(\eta, {\bf k}_1, \cdots, {\bf k}_n) = (2 \pi)^{3}~ \delta^3({\bf k}_1 + \cdots + {\bf k}_n)~ 
 \tilde{\cal G}(\eta, {\bf k}_1, \cdots, {\bf k}_n) \; .$$ It is worth mentioning that whenever we talk about the usual QFT, we shall be dealing with four dimensional Lorentzian momenta while whenever we talk about cosmological perturbation theory, we shall be dealing with three dimensional Euclidean momenta. At sufficiently high order in perturbation theory, one expects to encounter Feynman diagrams with loops. This issue, in cosmological perturbation theory has been studied in great detail in the last few years. Beginning with [@PhysRevD.72.043514], there was a debate about whether these loop corrections to the 