## Two-photon transitions in primordial hydrogen recombination

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Hirata, Christopher M.

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The subject of cosmological hydrogen recombination has received much
attention recently because of its importance to predictions for and
cosmological constraints from CMB observations. While the central role of the
two-photon decay 2s->1s has been recognized for many decades, high-precision
calculations require us to consider two-photon decays from the higher states
ns,nd->1s (n>=3). Simple attempts to include these processes in recombination
calculations have suffered from physical problems associated with sequences of
one-photon decays, e.g. 3d->2p->1s, that technically also produce two photons.
These correspond to resonances in the two-photon spectrum that are optically
thick, necessitating a radiative transfer calculation. We derive the
appropriate equations, develop a numerical code to solve them, and verify the
results by finding agreement with analytic approximations to the radiative
transfer equation. The related processes of Raman scattering and two-photon
recombination are included using similar machinery. Our results show that early
in recombination the two-photon decays act to speed up recombination, reducing
the free electron abundance by 1.3% relative to the standard calculation at
z=1300. However we find that some photons between Ly-alpha and Ly-beta are
produced, mainly by 3d->1s two-photon decay and 2s->1s Raman scattering. At
later times these photons redshift down to Ly-alpha, excite hydrogen atoms, and
act to slow recombination. Thus the free electron abundance is increased by
1.3% relative to the standard calculation at z=900. The implied correction to
the CMB power spectrum is neligible for the recently released WMAP and ACBAR
data, but at Fisher matrix level will be 7 sigma for Planck. [ABRIDGED]

Comment: Matches PRD accepted version. 28 pages, 12 figures

Comment: Matches PRD accepted version. 28 pages, 12 figures

##### Keywords

Astrophysics