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We present the 1.4GHz radio luminosity functions (RLFs) of galaxies in theCOSMOS field, measured above and below the $5\sigma$ detection threshold, usinga Bayesian model-fitting technique. The radio flux-densities from VLA-COSMOS3-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 activegalactic nuclei (AGN) and star-forming galaxy (SFG), in 10 redshift bins with apure luminosity evolution (PLE) model. We show that the evolution strength issimilar to literature values up to $z\sim 1.6$. Beyond $z\sim 2$, we find thatthe SFG RLF exhibits a negative evolution ($L^*$ moves to lower luminosities)due to the decrease in low stellar-mass sources in our stellar mass-limitedsample at high redshifts. From the RLF for SFGs, we determine the evolution inthe cosmic star-formation-rate density (SFRD), which we find to be consistentwith the established behaviour up to $z\sim 1$. Beyond $z\sim 1$ cosmic SFRDdeclines if one assumes an evolving infrared--radio correlation (IRRC), whereasit stays relatively higher if one adopts a constant IRRC. We find that the formof the relation between radio luminosity and SFR is therefore crucial inmeasuring the cosmic SFRD from radio data. We investigate the effects ofstellar mass on the total RLF by splitting our sample into low ($10^{8.5} \leqM/\mathrm{M}_{\odot} \leq 10^{10}$) and high ($M>10^{10}\,\mathrm{M}_{\odot}$)stellar-mass subsets. We find that the SFRD is dominated by sources in the highstellar masses bin, at all redshifts.

A deep radio view of the evolution of the cosmic star-formation rate density from a stellar-mass selected sample in VLA-COSMOS