CMB 3-point functions generated by nonlinearities at recombination

We study the 3-point functions generated at recombination in the squeezed triangle limit, when one mode has a wavelength much larger than the other two and is outside the horizon. The presence of the long-wavelength mode cannot change the physics inside the horizon but modifies how a late time observer sees the anisotropies. The effect of the long-wavelength mode can be divided into a redefinition of time and spatial scales, a Shapiro time delay and gravitational lensing. The separation is gauge dependent but helps develop intuition. We show that the resulting 3-point function corresponds to an $f_{\mathrm{N}\mathrm{L}}<1$ and that its shape is different from that created by the $f_{\mathrm{N}\mathrm{L}}$ (or local) model.