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 five larger than the perturbations in
baryon density. We do a thorough analysis of the second order anisotropies
generated in the cosmic microwave background (CMB) due to perturbations in the
electron number density. We show that solving the second order Boltzmann
equation for photons is equivalent to solving the first + 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 l 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 non-Gaussianity
parameter f_{NL}~ -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 l_{max}=2500.
