Ly alpha escape during cosmological hydrogen recombination: the 3d-1s
  and 3s-1s two-photon processes
  We give a formulation of the radiative transfer equation for Lyman alpha
photons which allows us to include the two-photon corrections for the 3s-1s and
3d-1s decay channels during cosmological hydrogen recombination. We use this
equation to compute the corrections to the Sobolev escape probability for Lyman
alpha photons during hydrogen recombination, which then allow us to calculate
the changes in the free electron fraction and CMB temperature and polarization
power spectra. We show that the effective escape probability changes by DP/P ~+
11% at z~1400 in comparison with the one obtained using the Sobolev
approximation. This speeds up of hydrogen recombination by DN_e/N_e ~- 1.6% at
z~1190, implying |DC_l/C_l| ~1%-3% at l >~ 1500 with shifts in the positions of
the maxima and minima in the CMB power spectra. These corrections will be
important for the analysis of future CMB data.
  The total correction is the result of the superposition of three independent
processes, related to (i) time-dependent aspects of the problem, (ii)
corrections due to quantum mechanical deviations in the shape of the emission
and absorption profiles in the vicinity of the Lyman alpha line from the normal
Lorentzian, and (iii) a thermodynamic correction factor, which occurs to be
very important. All these corrections are neglected in the
Sobolev-approximation, but they are important in the context of future CMB
observations. All three can be naturally obtained in the two-photon formulation
of the Lyman alpha absorption process. However, the corrections (i) and (iii)
can also be deduced in the normal '1+1' photon language, without necessarily
going to the two-photon picture. Therefore only (ii) is really related to the
quantum mechanical aspects of the two-photon process (abridged)
