  We derive the full set of second-order equations governing the evolution of
cosmological perturbations, including the effects of the first-order electron
number density perturbations, \delta_e. We provide a detailed analysis of the
perturbations to the recombination history of the universe and show that a
perturbed version of the Peebles effective 3-level atom is sufficient for
obtaining the evolution of \delta_e for comoving wavenumbers smaller than
1Mpc^{-1}. We calculate rigorously the perturbations to the Ly\alpha escape
probability and show that to a good approximation it is governed by the local
baryon velocity divergence. For modes shorter than the photon diffusion scale,
we find that \delta_e is enhanced during recombination by a factor of roughly 5
relative to other first-order quantities sourcing the CMB anisotropies at
second order. Using these results, in a companion paper we calculate the CMB
bispectrum generated during recombination.
