Single-Field Consistency relation and $\delta N$-Formalism

Understand

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.