# Cosmological hydrogen recombination

Much of our knowledge about the cosmic energy budget comes from the statistical properties of CMB anisotropies, roughly speaking produced at a redshift $z\sim 1100$, when the universe became optically thin to Thomson scattering, shortly after half of the hydrogen in the universe became neutral (hydrogen ‘recombination‘). With ever better measurements of CMB anisotropies in hand (thanks, for example, to experiments like Planck and ongoing ground-based CMB experiments), it has become exceedingly important to compute the dynamics of recombination with increasing precision and accuracy, including a variety of atomic physics and radiative transfer processes.

The cosmologically uninitiated reader might be delighted to learn that half of the neutral hydrogen produced before the first stars reionized the universe was produced in the `forbidden’ 2s-1s transition of neutral hydrogen. Even more remarkable is the fact that as of 2015, the best constraint to the rate of this transition now comes from measurements of CMB anisotropies, and not lab experiments.

Building upon the classic work of Zeldovich, Kurt, Sunyaev, and Peebles, and an update by Seager, Sasselov, and Scott, researchers around the world undertook a systematic program to compute recombination with sufficient precision for Planck data to be used to accurately probe primordial initial conditions and cosmological parameters. The motivation for this program is shown schematically in the cartoon at the top of this page.

Some of the relevant physical processes include two-photon radiative processes, deviations from statistical equilibrium between states with the same energy level but different angular momentum, deviations from a thermal radiation field, photon feedback, diffusion through the Lyman $\alpha$ line, and others. My contribution to this work (described in my Ph.D thesis and several papers) consisted of

• Developing sparse matrix methods and new recombination code (RecSparse), which tracks the populations of $10^{4}$ states at the same time, including transitions between states with the same principal quantum number $n$ but different angular momenta. Using this code, I (collaborating with Chris Hirata) established the convergence of hydrogen recombination with sufficient precision for Planck data analysis with maximum principal quantum number $n=128$. This result was later confirmed by Jens Chluba.
• Computing the impact of radiative quadrupole transitions at similarly high $n$.
• Showing that population inversion does happen in neutral hydrogen as it forms in the early universe, but with insufficient optical depth to produce laser radiation.

Our efforts helped determine the correction (to the code RecFast) applied in Planck data analysis to obtain robust cosmological results. Many of those who contributed to the execution of this program are shown in the picture below from the 2009 Orsay Recombination Workshop. Two precise, independent, and fast codes (that agree!) including all of these effects were written by Yacine Ali-Haïmoud & Jens Chluba. These recombination codes can now be readily run from within the CAMB CMB anisotropy power spectrum code.

Front: Dmitry Solovyev, Jose-Alberto Rubino-Martin, Martin Bucher, and Chris Hirata Back: Evgeny Kholupenko, Wan Yan Wong, Douglas Scott, Jens Chluba, Daniel Grin, and Yacine Ali-Haimoud. Not pictured: Silvia Galli, Ulrich Jentschura, Rashid Sunyaev, Leonti Labzowsky, Savely Karshenboim, John Forbes, Efsandiar Alizadeh, Geoffrey Vasil, and Jonathan Dursi.