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Radio wavelengths offer a unique possibility to trace the totalstar-formation rate (SFR) in galaxies, both obscured and unobscured. To probethe dust-unbiased star-formation history, an accurate measurement of the radioluminosity function (LF) for star-forming galaxies (SFGs) is crucial. We makeuse of an SFG sample (5900 sources) from the Very Large Array (VLA) COSMOS 3GHz data to perform a new modeling of the radio LF. By integrating theanalytical LF, we aim to calculate the history of the cosmic SFR density (SFRD)from $z\sim5$ onwards. For the first time, we use both models of the pureluminosity evolution (PLE) and joint luminosity+density evolution (LADE) to fitthe LFs directly to the radio data using a full maximum-likelihood analysis,considering the sample completeness correction. We also incorporate updatedobservations of local radio LFs and radio source counts into the fittingprocess to obtain additional constraints. We find that the PLE model cannot beused to describe the evolution of the radio LF at high redshift ($z>2$). Byconstruct, our LADE models can successfully fit a large amount of data on radioLFs and source counts of SFGs from recent observations. We therefore concludethat density evolution is genuinely indispensable in modeling the evolution ofSFG radio LFs. Our SFRD curve shows a good fit to the SFRD points derived byprevious radio estimates. In view of the fact that our radio LFs are notbiased, as opposed those of previous studies performed by fitting the $1/V_{\rmmax}$ LF points, our SFRD results should be an improvement on these previousestimates. Below $z\sim1.5$, our SFRD matches a published multiwavelengthcompilation, while our SFRD turns over at a slightly higher redshift($2<z<2.5$) and falls more rapidly out to high redshift.

Constraints on cosmic star formation history via a new modeling of the radio luminosity function of star-forming galaxies