2022ApJ...941...10V

We make use of ultra-deep 3 GHz Karl G. Jansky Very Large Array (VLA) observations of the COSMOS field from the multiband COSMOS-XS survey to infer radio luminosity functions (LFs) of star-forming galaxies (SFGs). Using ∼1300 SFGs with redshifts out to z ∼ 4.6, and fixing the faint and bright end shape of the radio LF to the local values, we find a strong redshift trend that can be fitted by pure luminosity evolution with the luminosity parameter given by α_L ∝ (3.40 ± 0.11) - (0.48 ± 0.06)z. We then combine the ultra-deep COSMOS-XS data set with the shallower VLA-COSMOS 3 GHz large project data set over the wider COSMOS field in order to fit for joint density+luminosity evolution, finding evidence for significant density evolution. By comparing the radio LFs to the observed far-infrared and ultraviolet (UV) LFs, we find evidence of a significant underestimation of the UV LF by 22% ± 14% at high redshift (3.3 < z < 4.6, integrated down to $0.03\,{L}_{z=3}^{\star }$). We derive the cosmic star formation rate density (SFRD) by integrating the fitted radio LFs and find that the SFRD rises up to z ∼ 1.8 and then declines more rapidly than previous radio-based estimates. A direct comparison between the radio SFRD and a recent UV-based SFRD, where we integrate both LFs down to a consistent limit ($0.038\,{L}_{z=3}^{\star }$), reveals that the discrepancy between the radio and UV LFs translates to a significant (∼1 dex) discrepancy in the derived SFRD at z > 3, even assuming the latest dust corrections and without accounting for optically dark sources.