Power-counting during single-field slow-roll inflation
  We elucidate the counting of the relevant small parameters in inflationary
perturbation theory. Doing this allows for an explicit delineation of the
domain of validity of the semi-classical approximation to gravity used in the
calculation of inflationary correlation functions. We derive an expression for
the dependence of correlation functions of inflationary perturbations on the
slow-roll parameter $\epsilon = -\dot{H}/H^2$, as well as on $H/M_p$, where $H$
is the Hubble parameter during inflation. Our analysis is valid for
single-field models in which the inflaton can traverse a Planck-sized range in
field values and where all slow-roll parameters have approximately the same
magnitude. As an application, we use our expression to seek the boundaries of
the domain of validity of inflationary perturbation theory for regimes where
this is potentially problematic: models with small speed of sound and models
allowing eternal inflation.
