  We show that the RG flow equation for the cosmological constant (CC) receives
contributions (in addition to those coming from the CC the Einstein-Hilbert
term and $R^{2}$ and $R_{\mu\nu}^{2}$ terms) only from terms with just two
powers of curvature, but having also powers of the covariant derivative, in the
Wilsonian effective action. In pure gravity our argument implies that just
considering $f(R)$ theories will miss this effect which arises from terms such
as $"R"\square^{n}"R",\,n=0,1,2,\ldots$. We expect similar contributions for
the flow equation of the Einstein-Hilbert term as well. Finally we argue that
the perturbative ghosts coming from curvature squared terms in the action are
in fact spurious since they are at the cutoff scale and can be removed by
(cutoff dependent) field redefinitions.
