  Many statistics available to constrain non-Gaussianity from inflation are
simplest to use under the assumption that the curvature correlation functions
are hierarchical. That is, if the n-point function is proportional to the (n-1)
power of the two-point function amplitude and the fluctuations are small, the
probability distribution can be approximated by expanding around a Gaussian in
moments. However, single-field inflation with higher derivative interactions
has a second small number, the sound speed, that appears in the problem when
non-Gaussianity is significant and changes the scaling of correlation
functions. Here we examine the structure of correlation functions in the most
general single scalar field action with higher derivatives, formalizing the
conditions under which the fluctuations can be expanded around a Gaussian
distribution. We comment about the special case of the Dirac-Born-Infeld
action.
