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

TL;DR

This paper introduces a new computational code, RecSparse, to accurately model hydrogen recombination including extremely high-n states, crucial for precise CMB analysis and cosmological parameter estimation.

Contribution

The paper presents RecSparse, a novel multi-level-atom code that efficiently includes hydrogen's high-n states and quadrupole transitions, improving recombination history calculations.

Findings

Including high-n states affects CMB power spectrum predictions.

RecSparse achieves convergence of recombination histories up to n=250.

Errors from low n_max values can significantly bias cosmological parameters.

Abstract

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 re-ionization. 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 non-equilibrium effects at late times (z<900). The inclusion of extremely high-n (n>100) states of hydrogen is then computationally challenging, preventing until now a determination of the maximum n needed to predict CMB anisotropy spectra with sufficient accuracy for Planck. Here, results from a new multi-level-atom code (RecSparse) are presented. For the first time, `forbidden' quadrupole transitions of hydrogen are included, but shown to be negligible. RecSparse is designed to quickly calculate recombination histories including extremely high-n states in hydrogen. Histories for a sequence of values as high as n_max=250 are computed, keeping track of all angular momentum sublevels and energy shells of the hydrogen atom separately. Use of an insufficiently high n_max value (e.g., n_max=64) leads to errors (e.g., 1.8 sigma for Planck) in the predicted CMB power spectrum. Extrapolating errors, the resulting CMB anisotropy spectra are converged to 0.5 sigma at Fisher-matrix level for n_max=128, in the purely radiative case.