O-V-S-Z and friends: Non-Gaussianity from inhomogeneous reionization

We calculate the cosmic microwave background (CMB) bispectrum due to inhomogeneous reionization. We calculate all the terms that can contribute to the bispectrum that are products of first order terms on all scales in conformal Newtonian gauge. We also correctly account for the de-correlation between the matter density and initial conditions using perturbation theory up to third order. We find that the bispectrum is of local type as expected. For a reasonable model of reionization, in which the Universe is completely ionized by redshift z_{ri} ~ 8 with optical depth to the last scattering surface \tau_0=0.087 the signal to noise for detection of the CMB temperature bispectrum is S/N ~ 0.1 and confusion in the estimation of primordial non-Gaussianity is f_{NL} ~ -0.1. For an extreme model with z_{ri} ~ 12.5, \tau_0=0.14 we get S/N ~ 0.5 and f_{NL} ~ -0.2.