Cosmology with Recombination Spectrum
  Precision measurement of the cosmological recombination spectrum can provide
an entire new window to look at the early universe. We aim to quantify the
information hidden in the cosmological recombination spectrum and for this
purpose we have developed a new code following the algorithm proposed in
Ali-Haimoud and Hirata (2010), Ali-Haimoud (2013). Our code is closely based on
the COSMOSPEC code [Chluba and Ali-Haimoud (2016)]. We find, using Fisher
information matrix and assuming that the foregrounds can be subtracted by using
higher or lower frequency channels and spatial information, that going beyond
the detection will need an experiment with sensitivity $25$ times better
compared to the proposed experiment PIXIE. Such an experiment will be able to
measure the cosmological parameters with a precision that is competitive with
the CMB anisotropy experiments. The best constrainted parameter is baryon
energy density, $\Omega_{\rm b}$, which can be nailed down with incredible
precision in principle. We also show that the shape of the hydrogen lines is
connected to the speed of the hydrogen recombination, with the peaks of the
recombination lines coinciding with the peak of the recombination rate. In
general, the shape of the lines encodes information about the rate of
recombination as a function of redshift.
