The CMB bispectrum in the squeezed limit

The CMB bispectrum generated by second-order effects at recombination can be calculated analytically when one of the three modes has a wavelength much longer than the other two and is outside the horizon at recombination. This was pointed out in [1] and here we correct their results. We derive a simple formula for the bispectrum, fNLloc = −(1/6+cos 2θ)⋅(1−1/2⋅dln (lS2CS)/dln lS), where CS is the short scale spectrum and θ the relative orientation between the long and the short modes. This formula is exact and takes into account all effects at recombination, including recombination-lensing, but neglects all late-time effects such as ISW-lensing. The induced bispectrum in the squeezed limit is small and will negligibly contaminate the Planck search for a local primordial signal: this will be biased only by fNLloc ≈ −0.4. The above analytic formula includes the primordial non-Gaussianity of any single-field model. It also represents a consistency check for second-order Boltzmann codes: we find substantial agreement with the current version of the CMBquick code