Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primordial helium recombination III: Thomson scattering, isotope shifts,
  and cumulative results   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
$2^3P^o-1^1S$ 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 $x_e$.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an