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We give a formulation of the radiative transfer equation for Lyman alphaphotons which allows us to include the two-photon corrections for the 3s-1s and3d-1s decay channels during cosmological hydrogen recombination. We use thisequation to compute the corrections to the Sobolev escape probability for Lymanalpha photons during hydrogen recombination, which then allow us to calculatethe changes in the free electron fraction and CMB temperature and polarizationpower spectra. We show that the effective escape probability changes by DP/P ~+11% at z~1400 in comparison with the one obtained using the Sobolevapproximation. This speeds up of hydrogen recombination by DN_e/N_e ~- 1.6% atz~1190, implying |DC_l/C_l| ~1%-3% at l >~ 1500 with shifts in the positions ofthe maxima and minima in the CMB power spectra. These corrections will beimportant for the analysis of future CMB data.  The total correction is the result of the superposition of three independentprocesses, related to (i) time-dependent aspects of the problem, (ii)corrections due to quantum mechanical deviations in the shape of the emissionand absorption profiles in the vicinity of the Lyman alpha line from the normalLorentzian, and (iii) a thermodynamic correction factor, which occurs to bevery important. All these corrections are neglected in theSobolev-approximation, but they are important in the context of future CMBobservations. All three can be naturally obtained in the two-photon formulationof the Lyman alpha absorption process. However, the corrections (i) and (iii)can also be deduced in the normal '1+1' photon language, without necessarilygoing to the two-photon picture. Therefore only (ii) is really related to thequantum mechanical aspects of the two-photon process (abridged)

Ly alpha escape during cosmological hydrogen recombination: the 3d-1s and 3s-1s two-photon processes