  We present an investigation of radio luminosity functions (LFs) and number
counts based on the Karl G. Jansky Very Large Array-COSMOS 3 GHz Large Project.
The radio-selected sample of 7826 galaxies with robust optical/near-infrared
counterparts with excellent photometric coverage allows us to construct the
total radio LF since z~5.7. Using the Markov chain Monte Carlo algorithm, we
fit the redshift dependent pure luminosity evolution model to the data and
compare it with previously published VLA-COSMOS LFs obtained on individual
populations of radio-selected star-forming galaxies and galaxies hosting active
galactic nuclei classified on the basis of presence or absence of a radio
excess with respect to the star-formation rates derived from the infrared
emission. We find they are in excellent agreement, thus showing the reliability
of the radio excess method in selecting these two galaxy populations at radio
wavelengths. We study radio number counts down to submicrojansky levels drawn
from different models of evolving LFs. We show that our evolving LFs are able
to reproduce the observed radio sky brightness, even though we rely on
extrapolations toward the faint end. Our results also imply that no new
radio-emitting galaxy population is present below 1 ujy. Our work suggests that
selecting galaxies with radio flux densities between 0.1 and 10 ujy will yield
a star-forming galaxy in 90-95 % of the cases with a high percentage of these
galaxies existing around a redshift of z~2, thus providing useful constraints
for planned surveys with the Square Kilometer Array and its precursors.
