We compute the spectral distortions of the Cosmic Microwave
Background (CMB) arising during the epoch of cosmological hydrogen recombination within the standard cosmological (concordance) model for frequencies in the range 1 GHz - 3500 GHz.
We follow the evolution of the populations of the hydrogen levels including states up to principle quantum number n=30 in the redshift range 500 < z < 3500.
All angular momentum sub-states are treated individually, resulting in a
total number of 465 hydrogen levels. The evolution of the matter
temperature and the fraction of electrons coming from HeII are also
included.
We present a detailed discussion of the distortions arising from the
main dipolar transitions, e.g. Lyman and Balmer series, as well as the
emission due to the two-photon decay of the hydrogen 2s level.
Furthermore, we investigate the robusteness of the results against
changes in the number of shells considered.
The resulting spectral distortions have a characteristic oscillatory
behaviour, which might allow experimentalists to separate them from
other backgrounds. The relative distortion of the spectrum exceeds a
value of 10^{-7} at wavelengths longer than 21cm.
Our results also show the importance of detailed follow-up of the angular momentum sub-states, and their effect on the amplitude of the lines.
The effect on the residual electron fraction is only moderate, and
mainly occurs at low redshifts. The CMB angular power spectrum is changed by less than 1%.
Finally, our computations show that if the primordial
radiation field is described by a pure blackbody, then
there is no significant emission
from any hydrogen transition at redshifts greater than z ~ 2000.
This is in contrast to some earlier works, where the existence of a `pre-recombination' peak was claimed.