Abstract
We present the new recombination code HYREC-2, holding the same accuracy as
the state-of-the-art codes HYREC and COSMOREC and, at the same time, surpassing
the computational speed of the code RECFAST commonly used for CMB-anisotropy
data analyses. HYREC-2 is based on an effective 4-level atom model, accounting
exactly for the non-equilibrium of highly excited states of hydrogen, and very
accurately for radiative transfer effects with a correction to the
Lyman-$\alpha$ escape rate. The latter is computed with the original HYREC, and
tabulated, as a function of temperature, along with its derivatives with
respect to the relevant cosmological parameters. This enables the code to keep
the same accuracy as the original HYREC over the full 99.7% confidence region
of cosmological parameters currently allowed by Planck, while running in under
one millisecond on a standard laptop. Our code leads to no noticeable bias in
any cosmological parameters even in the case of an ideal cosmic-variance
limited experiment up to $\ell$ = 5000. Beyond CMB anisotropy calculations,
HYREC-2 will be a useful tool to compute various observables that depend on the
recombination and thermal history, such as the recombination spectrum or the
21-cm signal.
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