A Note on the Consistency Condition of Primordial Fluctuations
  We show that the squeezed limit of (N+1)-point functions of primordial
correlation functions in which one of the modes has a very small wavenumber can
be inferred from the spatial variation of locally measured N-point function. We
then show how in single clock inflation a long wavelength perturbation can be
re-absorbed in the background cosmology and how in computing correlation
functions the integrals of the interaction Hamiltonian are dominated by
conformal times of order of the short wavelength modes, when the long mode is
already outside of the horizon. This allows us to generalize the consistency
condition for N-point functions to the case in which the short wavelength
fluctuations are inside the horizon and derivatives acts on them. We further
discuss the consistency condition in the soft internal squeezed limit in which
in an (N+M)-point function with (N+M) short modes the sum of the first N modes
is a very soft momentum. These results are very useful to study infrared
effects in Inflation.
