Fast and accurate primordial hydrogen recombination theory

Yacine Ali-Haimoud

October 19, 2010

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Abstract: Cosmological hydrogen recombination has recently been the subject of renewed attention because of its importance for predicting the power spectrum of cosmic microwave background anisotropies. Correctly interpreting the upcoming data from the Planck satellite in terms of cosmological parameters indeed requires sub-percent accuracy in theoretical recombination histories. Two aspects are crucial to reach such an accuracy. At early times (z >~800), the dynamics of hydrogen recombination is controlled by the slow decays from the n=2 shell to the ground state, through two-photon decays from the 2s state and the highly self-absorbed Lyman alpha transition. Subtle radiative transfer effects must be accounted for in order to correctly calculate the rate of decays to the ground state of hydrogen. At late times, due to the decreasing abundance of free electrons and protons, an accurate recombination history must account for all the recombination pathways, and include excited states of hydrogen up to a very high principal quantum number n > 100. The cold radiation field at late times is not strong enough to maintain the angular momentum substates in statistical equilibrium, and they must therefore be followed separately. The traditional method of solution for the multi-level atom is very time consuming computationally and unpractical for inclusion in fast Markov chains for cosmological parameter estimation. In this talk I will present my recent work on a new method of solution, which allows to account for an arbitrarily large number of excited states, and is 5 to 6 orders of magnitude faster than the previously used method. I will also expose my recent work on radiative transfer effects and my current work on a fast and highly accurate recombination code.