Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How exactly did the Universe become neutral?   We present a refined treatment of H, He I, and He II recombination in the
early Universe. The difference from previous calculations is that we use
multi-level atoms and evolve the population of each level with redshift by
including all bound-bound and bound-free transitions. In this framework we
follow several hundred atomic energy levels for H, He I, and He II combined.
The main improvements of this method over previous recombination calculations
are: (1) allowing excited atomic level populations to depart from an
equilibrium distribution; (2) replacing the total recombination coefficient
with recombination to and photoionization from each level directly at each
redshift step; and (3) correct treatment of the He I atom, including the
triplet and singlet states. We find that the ionization fraction x_e = n_e/n_H
is approximately 10% smaller at redshifts <~800 than in previous calculations,
due to the non-equilibrium of the excited states of H, which is caused by the
strong but cool radiation field at those redshifts. In addition we find that He
I recombination is delayed compared with previous calculations, and occurs only
just before H recombination. These changes in turn can affect the predicted
power spectrum of microwave anisotropies at the few percent level. Other
improvements such as including molecular and ionic species of H, including
complete heating and cooling terms for the evolution of the matter temperature,
including collisional rates, and including feedback of the secondary spectral
distortions on the radiation field, produce negligible change to x_e. The lower
x_e at low z found in this work affects the abundances of H molecular and ionic
species by 10-25%. However this difference is probably not larger than other
uncertainties in the reaction rates.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg