  To characterise the cosmological evolution of the sources contributing to the
infrared extragalactic background, we have developped a phenomenological model
that constrains in a simple way the galaxy luminosity function evolution with
the redshift, and fits all the existing source counts and redshift
distributions, Cosmic Infrared Background intensity and fluctuations
observations, from the mid-infrared to the submillimetre range. The model is
based on template spectra of starburst and normal galaxies, and on the local
infrared luminosity function. Although the Cosmic Infrared Background can be
modeled with very different luminosity functions as long as the radiation
production with redshift is the right one, the number counts, and the
anisotropies of the unresolved background, imply that the luminosity function
must change dramatically with redshift, with a rapid evolution of the
high-luminosity sources (L>3 10^{11} L_{\odot}) from z=0 to z=1 which then stay
rather constant up to redshift 5. The derived evolution of the IR luminosity
function may be linked to a bimodal star formation process, one associated with
the quiescent and passive phase of the galaxy evolution and one associated with
the starburst phase, trigerred by merging and interactions. The latter
dominates the infrared and submillimetre ouput energy of the Universe.
  The model is intended as a convenient tool to plan further observations, as
illustrated through predictions for Herschel, Planck and ALMA observations. Our
model predictions for given wavelengths, together with some usefull routines,
are available for general use.
