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We explore the imprint of the cosmological hydrogen recombination lines onthe power spectrum of the cosmic microwave background (CMB). In particular, wefocus our analysis in the three strongest lines for the Balmer, Paschen andBrackett series of hydrogen. We expect changes in the angular power spectrumdue to these lines on the level of $0.3 \mu K$ for the H$\alpha$ line, beingmaximum at small angular scales ($\ell \approx 870$). The morphology of thesignal is very rich. It leads to relatively narrow spectral features ($\Delta\nu / \nu \sim 10^{-1}$), with several regions in the power spectrum showing acharacteristic change of sign of the effect as we probe different redshifts ordifferent multipoles by measuring the power spectrum at different frequencies.It also has a very peculiar dependence on the multipole scale, connected withthe details of the transfer function at the epoch of scattering. In order tocompute the optical depths for these transitions, we have evolved numericallythe populations of the levels of the hydrogen atom during recombination,treating simultaneously the evolution of helium. For the hydrogen atom, wefollow each angular momentum state separately, up to the level n=10.Foregrounds and other frequency dependent contaminants, as Rayleigh scattering,may be a important limitation for these measurements, although the peculiarfrequency and angular dependences of the effect which we are discussing mightpermit to separate it. Detection of this signal using future narrow-bandspectral observations can give information about the details of how the cosmicrecombination proceeds, and how Silk damping operates during recombination.

The imprint of cosmological hydrogen recombination lines on the power spectrum of the CMB