More on crinkles in the last scattering surface

Inhomogeneous recombination can give rise to perturbations in the electron number density which can be a factor of 5 larger than the perturbations in baryon density. We do a thorough analysis of the second order anisotropies generated in the cosmic microwave background due to perturbations in the electron number density. We show that solving the second order Boltzmann equation for photons is equivalent to solving the firstþ second order Boltzmann equations and then taking the second order part of the solution. We find the approximate solution to the photon Boltzmann hierarchy in ‘ modes and show that the contributions from inhomogeneous recombination to the second order monopole, dipole, and quadrupole are numerically small. We also point out that perturbing the electron number density in the first order tight coupling and damping solutions for the monopole, dipole, and quadrupole is not equivalent to solving the second order Boltzmann equations for inhomogeneous recombination. Finally, we confirm our result in a previous paper that inhomogeneous recombination gives rise to a local type nonGaussianity parameter fNL 1. The signal to noise for the detection of the temperature bispectrum generated by inhomogeneous recombination is 1 for an ideal full sky experiment measuring modes up to ‘max 1⁄4 2500.