CMB 3-point functions generated by non-linearities 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_NL < 1 and that its shape is different from that created by the f_NL (or local) model.

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