  Cosmological constraints from the cosmic microwave background (CMB)
anisotropies rely on accurate theoretical calculations of the cosmic
recombination history. Recent work has emphasized the importance of radiative
transfer calculations due to the high optical depth in the HI Lyman lines.
Transfer in the Lyman-alpha line is dominated by true emission and absorption,
Hubble expansion, and resonant scattering. Resonant scattering causes photons
to diffuse in frequency due to random kicks from the thermal velocities of
hydrogen atoms, and also to drift toward lower frequencies due to energy loss
via atomic recoil. Past analyses of Lyman-alpha transfer during the
recombination era have either considered a subset of these processes, ignored
time dependence, or incorrectly assumed identical emission and absorption
profiles. We present here a fully time-dependent radiative transfer calculation
of the Lyman-alpha line including all of these processes, and compare it to
previous results that ignored the resonant scattering. We find a faster
recombination due to recoil enhancement of the Lyman-alpha escape rate, leading
to a reduction in the free electron density of 0.45% at z=900. This results in
an increase in the small-scale CMB power spectrum that is negligible for the
current data but will be a 0.9 sigma correction for Planck. We discuss the
reasons why we find a smaller correction than some other recent computations.
