extremely careful (in this context, see [@PhysRevD.72.043514; @PhysRevD.74.023508; @SZ2010]). In cosmological perturbation theory, one is studying fluctuations around a time dependent background solution, thus, the action of these fluctuations is not Lorentz invariant. Thus, we can not simply list all the possible terms in the action (moreover, since the typical interactions are irrelevant, infinite couterterms shall be required). All this ensures that it is difficult to spot the couterterms in cosmological perturbation theory. Given this situation, one could ask, given a correlator (e.g. the two-point function), which counterterms shall we need to renormalize it at one loop?

From our experience in usual QFT, we are used to spotting the counterterms by looking at the expression for dimensionally regulated correlators. This is because the expression for the correlator (with external lines amputed) is of the form $\sum_n c_n (k^2)^n$ (where, $k$ is the Lorentzian momentum of the external line) i.e., a polynomial in the external momenta with divergent coefficients.

Unlike in usual QFT, in cosmological perturbation theory, the dimensionally regulated logarithmically divergent two-point correlator (for external momentum $k$) is (at late times) of the form $$\left[ \sum_n c_n (|{\bf k}|)^n \right] \left[\sum_m a_m (-k \eta)^m \right] \; ,$$

where, $k$ is 