can be performed and the emphasis usually is on the non-trivial logarithmic running which may turn up (see, e.g., [@PhysRevD.72.043514]). E.g. Senatore and Zaldarriaga [@SZ2010] have studied renormalization of two-point function in cosmological perturbation theory. Their main focus has been on the nature of logarithmic running. In contrast, in the present work, we look at the actual process of renormalization and the associated subtleties.

We begin in Sec. \[sec:usual\_qft\] by recalling how counterterms are found in usual QFT. Then, in sec. \[sec:cosmo\_pert\], after introducing the particular regime of effective field theory of inflation for which we present the arguments about the UV divergent two-point correlator, we shall describe how the case of cosmological perturbation theory is so different from the usual QFT in so peculiar a way. We summarize the results in Sec. \[sec:summary\]. We have set $\hbar = c = 1$.

Counterterms in usual QFT: {#sec:usual_qft}
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In usual QFT, LSZ reduction formula ensures that the most relevant quantity to evaluate is the vacuum expectation value of time ordered product of the Heisenberg picture fields. While evaluating the Fourier transforms of such correlators, at sufficiently high order in perturbation theory one encounters UV divergences. E.g. one could encounter quadratically 