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We present an analysis of the radio properties of large samples of LymanBreak Galaxies (LBGs) at $z \sim 3$, 4, and 5 from the COSMOS field. The medianstacking analysis yields a statistical detection of the $z \sim 3$ LBGs (U-banddrop-outs), with a 1.4 GHz flux density of $0.90 \pm 0.21 \mu$Jy. The stackedemission is unresolved, with a size $< 1"$, or a physical size $< 8$kpc. Thetotal star formation rate implied by this radio luminosity is $31\pm 7$$M_\odot$ year$^{-1}$, based on the radio-FIR correlation in low redshift starforming galaxies. The star formation rate derived from a similar analysis ofthe UV luminosities is 17 $M_\odot$ year$^{-1}$, without any correction for UVdust attenuation. The simplest conclusion is that the dust attenuation factoris 1.8 at UV wavelengths. However, this factor is considerably smaller than thestandard attenuation factor $\sim 5$, normally assumed for LBGs. We discusspotential reasons for this discrepancy, including the possibility that the dustattenuation factor at $z \ge 3$ is smaller than at lower redshifts. Conversely,the radio luminosity for a given star formation rate may be systematicallylower at very high redshift. Two possible causes for a suppressed radioluminosity are: (i) increased inverse Compton cooling of the relativisticelectron population due to scattering off the increasing CMB at high redshift,or (ii) cosmic ray diffusion from systematically smaller galaxies. The radiodetections of individual sources are consistent with a radio-loud AGN fractionof 0.3%. One source is identified as a very dusty, extreme starburst galaxy (a'submm galaxy').

Star formation rates in Lyman break galaxies: radio stacking of LBGs in the COSMOS field and the sub-$\mu$Jy radio source population