Cosmological hydrogen recombination: The effect of extremely high-n states

Calculations of cosmological hydrogen recombination are vital for the extraction of cosmological parameters from cosmic microwave background (CMB) observations, and for imposing constraints to inflation and reionization. The Planck mission and future experiments will make high precision measurements of CMB anisotropies at angular scales as small as ℓ∼2500, necessitating a calculation of recombination with fractional accuracy of ≈10^(-3). Recent work on recombination includes two-photon transitions from high excitation states and many radiative transfer effects. Modern recombination calculations separately follow angular momentum sublevels of the hydrogen atom to accurately treat nonequilibrium effects at late times (z