[Abridged] We present a comprehensive investigation of the cosmological evolution of the luminosity function (LF) of galaxies and active galactic nuclei (AGN) in the infrared (IR). Based on the observed dichotomy in the ages of stellar populations of early-type galaxies on one side and late-type galaxies on the other, the model interprets the epoch-dependent LFs at z geq 1.5 using a physical model for the evolution of proto-spheroidal galaxies and of the associated AGNs, while IR galaxies at z<1.5 are interpreted as being mostly late-type cold (normal) and warm (starburst) galaxies. As for proto-spheroids, in addition to the epoch-dependent LFs of stellar and AGN components separately, we have worked out the evolving LFs of these objects as a whole (stellar plus AGN component). The model provides a physical explanation for the observed positive evolution of both galaxies and AGNs up to z simeq 2.5 and for the negative evolution at higher redshifts, for the sharp transition from Euclidean to extremely steep counts at (sub-)mm wavelengths, as well as the (sub-)mm counts of strongly lensed galaxies, that are hard to account for by alternative, physical or phenomenological, approaches. The evolution of late-type galaxies and of z<1.5 AGNs is described using a parametric phenomenological approach. The modeled AGN contributions to the counts and to the cosmic infrared background (CIB) are always subdominant with maximal at mid-IR wavelengths. The model provides a good fit to the multi-wavelength (from the mid-IR to millimeter waves) data on LFs at different redshifts and on number counts (both global and per redshift slices). A prediction of the present model is a systematic variation with wavelength of the populations dominating the counts and the contributions to the CIB intensity. The implied specific trend for cross-wavelength CIB power spectra is found to be in good agreement with the data.
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