Spectral distortions to the cosmic microwave background from the recombination of hydrogen and helium

The recombination of hydrogen and helium at z ∼ 1000-7000 gives unavoidable distortions to the cosmic microwave background (CMB) spectrum. We present a detailed calculation of the line intensities arising from the Lyman a (Lya) (2p-ls) and two-photon (2s-ls) transitions for the recombination of hydrogen, as well as the corresponding lines from helium. We give an approximate formula for the strength of the main recombination line distortion on the CMB in different cosmologies; this peak occurring at about 170 μm. We also find a previously undescribed long-wavelength peak (which we call the pre-recombination peak) from the lines of the 2p-1 s transitions, which are formed before significant recombination of the corresponding atoms occurred. Detailed calculations of the two-photon emission-line shapes are presented here for the first time. The frequencies of the photons emitted from the two-photon transition have a wide spectrum and this causes the location of the peak of the two-photon line of hydrogen to be located almost at the same wavelength as the main Lya peak. The helium lines also give distortions at similar wavelengths, so that the combined distortion has a complex shape. The detection of this distortion would provide direct supporting evidence that the Universe was indeed once a plasma. Moreover, the distortions are a sensitive probe of physics during the time of recombination. Although the spectral distortion is overwhelmed by dust emission from the Galaxy, and is maximum at wavelengths roughly where the cosmic far-infrared background peaks, it may be able to tailor an experiment to detect its non-trivial shape.