  We describe a simple way of incorporating fluctuations of the Hubble scale
during the horizon exit of scalar perturbations into the delta N formalism. The
dominant effect comes from the dependence of the Hubble scale on low-frequency
modes of the inflaton. This modifies the coefficient of the log-enhanced term
appearing in the curvature spectrum at second order in field fluctuations. With
this modification, the relevant coefficient turns out to be proportional to the
second derivative of the tree-level spectrum with respect to the inflaton phi
at horizon exit. A logarithm with precisely the same coefficient appears in a
calculation of the log-enhancement of the curvature spectrum based purely on
the geometry of the reheating surface. We take this agreement as strong support
for the proposed implementation of the delta N formalism. Moreover, our
analysis makes it apparent that the log-enhancement of the inflationary
power-spectrum is indeed physical if this quantity is defined using a global
coordinate system on the reheating surface (or any other post-inflationary
surface of constant energy density). However, it can be avoided by defining the
spectrum using invariant distances on this surface.
