Lyman-alpha transfer in primordial hydrogen recombination

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.