  We present the first fast and detailed computation of the cosmological
recombination radiation released during the hydrogen (redshift z ~ 1300) and
helium (z ~ 2500 and z ~ 6000) recombination epochs, introducing the code
CosmoSpec. Our computations include important radiative transfer effects,
500-shell bound-bound and free-bound emission for all three species, the
effects of electron scattering and free-free absorption as well as interspecies
(HeII --> HeI --> HI) photon feedback. The latter effect modifies the shape and
amplitude of the recombination radiation and CosmoSpec improves significantly
over previous treatments of it. Utilizing effective multilevel atom and
conductance approaches, one calculation takes only ~ 15 seconds on a standard
laptop as opposed to days for previous computations. This is an important step
towards detailed forecasts and feasibility studies considering the detection of
the cosmological recombination lines and what one may hope to learn from the ~
6.1 photons emitted per hydrogen atom in the three recombination eras. We
briefly illustrate some of the parameter dependencies and discuss remaining
uncertainties in particular related to collisional processes and the neutral
helium atom model.

Cosmology and Nongalactic Astrophysics