  We present the 1.4GHz radio luminosity functions (RLFs) of galaxies in the
COSMOS field, measured above and below the $5\sigma$ detection threshold, using
a Bayesian model-fitting technique. The radio flux-densities from VLA-COSMOS
3-GHz data, are extracted at the position of stellar mass-limited near-infrared
(NIR) galaxies. We fit a local RLF model, which is a combination of active
galactic nuclei (AGN) and star-forming galaxy (SFG), in 10 redshift bins with a
pure luminosity evolution (PLE) model. We show that the evolution strength is
similar to literature values up to $z\sim 1.6$. Beyond $z\sim 2$, we find that
the SFG RLF exhibits a negative evolution ($L^*$ moves to lower luminosities)
due to the decrease in low stellar-mass sources in our stellar mass-limited
sample at high redshifts. From the RLF for SFGs, we determine the evolution in
the cosmic star-formation-rate density (SFRD), which we find to be consistent
with the established behaviour up to $z\sim 1$. Beyond $z\sim 1$ cosmic SFRD
declines if one assumes an evolving infrared--radio correlation (IRRC), whereas
it stays relatively higher if one adopts a constant IRRC. We find that the form
of the relation between radio luminosity and SFR is therefore crucial in
measuring the cosmic SFRD from radio data. We investigate the effects of
stellar mass on the total RLF by splitting our sample into low ($10^{8.5} \leq
M/\mathrm{M}_{\odot} \leq 10^{10}$) and high ($M>10^{10}\,\mathrm{M}_{\odot}$)
stellar-mass subsets. We find that the SFRD is dominated by sources in the high
stellar masses bin, at all redshifts.

Astrophysics of Galaxies