Single-Field Consistency relation and $\delta N$-Formalism
  According to the equivalence principal, the long wavelength perturbations
must not have any dynamical effect on the short scale physics up to ${\cal O}
(k_L^2/k_s^2)$. Their effect can be always absorbed to a coordinate
transformation locally. So any physical effect of such a perturbation appears
only on scales larger than the scale of the perturbation. The bispectrum in the
squeezed limit of the curvature perturbation in single-field slow-roll
inflation is a good example, where the long wavelength effect is encoded in the
spectral index through Maldacena's consistency relation. This implies that one
should be able to derive the bispectrum in the squeezed limit without resorting
to the in-in formalism in which one computes perturbative corrections
field-theoretically. In this short paper, we show that the $\delta N$ formalism
as it is, or more generically the separate universe approach, when applied
carefully can indeed lead to the correct result for the bispectrum in the
squeezed limit. Hence despite the common belief that the $\delta N$ formalism
is incapable of recovering the consistency relation within itself, it is in
fact self-contained and consistent.
