Primordial helium recombination III: Thomson scattering, isotope shifts, and cumulative results

Abstract

Upcoming precision measurements of the temperature anisotropy of the cosmic microwave background (CMB) at high multipoles will need to be complemented by a more complete understanding of recombination, which determines the damping of anisotropies on these scales. This is the third in a series of papers describing an accurate theory of HeI and HeII recombination. Here we describe the effect of Thomson scattering, the ${}^3$He isotope shift, the contribution of rare decays, collisional processes, and peculiar motion. These effects are found to be negligible: Thomson and ${}^3$He scattering modify the free electron fraction $x_e$ at the level of several $\times 10^{-4}$. The uncertainty in the $2^3{P}^o-1^{1}S$ rate is significant, and for conservative estimates gives uncertainties in $x_e$ of order $10^{-3}$. We describe several convergence tests for the atomic level code and its inputs, derive an overall $C_{\ell }$ error budget, and relate shifts in $x_e(z)$ to the changes in $C_{\ell }$, which are at the level of 0.5% at $\ell =3000$. Finally, we summarize the main corrections developed thus far. The remaining uncertainty from known effects is $\sim 0.3$ in $x_e$.

arXiv comment19 pages, 15 figures, to be submitted to PRD

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