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We provide a coherent, uniform measurement of the evolution of thelogarithmic star formation rate (SFR) - stellar mass ($M_*$) relation, calledthe main sequence of star-forming galaxies (MS), for galaxies out to $z\sim5$.We measure the MS using mean stacks of 3 GHz radio continuum images to deriveaverage SFRs for $\sim$200,000 mass-selected galaxies at $z>0.3$ in the COSMOSfield. We describe the MS relation adopting a new model that incorporates alinear relation at low stellar mass (log($M_*$/M$_\odot$)$<$10) and aflattening at high stellar mass that becomes more prominent at low redshift($z<1.5$). We find that the SFR density peaks at $1.5<z<2$ and at each epochthere is a characteristic stellar mass ($M_* = 1 - 4 \times10^{10}\mathrm{M}_\odot$) that contributes the most to the overall SFR density.This characteristic mass increases with redshift, at least to $z\sim2.5$. Wefind no significant evidence for variations in the MS relation for galaxies indifferent environments traced by the galaxy number density at $0.3<z<3$, norfor galaxies in X-ray groups at $z\sim0.75$. We confirm that massivebulge-dominated galaxies have lower SFRs than disk-dominated galaxies at afixed stellar mass at $z<1.2$. As a consequence, the increase inbulge-dominated galaxies in the local star-forming population leads to aflattening of the MS at high stellar masses. This indicates that"mass-quenching" is linked with changes in the morphological composition ofgalaxies at a fixed stellar mass.

The VLA-COSMOS 3 GHz Large Project: Evolution of specific star formation rates out to $z\sim5$