Star formation and accretion onto supermassive black holes in the nuclei of galaxies are the two most energetic processes in the Universe, producing the bulk of the observed emission throughout its history. We simulated the luminosity functions of star-forming and active galaxies for spectral lines that are thought to be good spectroscopic tracers of either phenomenon, as a function of redshift. We focused on the infrared (IR) and sub-millimeter domains, where the effects of dust obscuration are minimal. Using three different and independent theoretical models for galaxy formation and evolution, constrained by multi-wavelength luminosity functions, we computed the number of star-forming and active galaxies per IR luminosity and redshift bin. We converted the continuum luminosity counts into spectral line counts using relationships that we calibrated on mid- and far-IR spectroscopic surveys of galaxies in the local universe. Our results demonstrate that future facilities optimized for survey-mode observations, i.e., the Space Infrared Telescope for Cosmology and Astrophysics (SPICA) and the Cerro Chajnantor Atacama Telescope (CCAT), will be able to observe thousands of z>1 galaxies in key fine-structure lines, e.g., [SiII], [OI], [OIII], [CII], in a half-square-degree survey, with one hour integration time per field of view. Fainter lines such as [OIV], [NeV] and H_2 (0-0)S1 will be observed in several tens of bright galaxies at 1<z<2, while diagnostic diagrams of active-nucleus vs star-formation activity will be feasible even for normal z~1 galaxies. We discuss the new parameter space that these future telescopes will cover and that strongly motivate their construction.
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