Effective conductance method for the primordial recombination spectrum
  As atoms formed for the first time during primordial recombination, they
emitted bound-bound and free-bound radiation leading to spectral distortions to
the cosmic microwave background. These distortions might become observable in
the future with high-sensitivity spectrometers, and provide a new window into
physical conditions in the early universe. The standard multilevel atom method
habitually used to compute the recombination spectrum is computationally
expensive, impeding a detailed quantitative exploration of the information
contained in spectral distortions thus far. In this work it is shown that the
emissivity in optically thin allowed transitions can be factored into a
computationally expensive but cosmology-independent part and a computationally
cheap, cosmology-dependent part. The slow part of the computation consists in
pre-computing temperature-dependent effective "conductances", linearly relating
line or continuum intensity to departures from Saha equilibrium of the
lowest-order excited states (2s and 2p), that can be seen as "voltages". The
computation of these departures from equilibrium as a function of redshift is
itself very fast, thanks to the effective multilevel atom method introduced in
an earlier work. With this factorization, the recurring cost of a single
computation of the recombination spectrum is only a fraction of a second on a
standard laptop, more than four orders of magnitude shorter than standard
computations. The spectrum from helium recombination can be efficiently
computed in an identical way, and a fast code computing the full primordial
recombination spectrum with this method will be made publicly available soon.
