We present an analysis of the radio properties of large samples of Lyman Break Galaxies ( LBGs ) at z \sim 3 , 4 , and 5 from the COSMOS field .
The median stacking analysis yields a statistical detection of the z \sim 3 LBGs ( U-band drop-outs ) , with a 1.4 GHz flux density of 0.90 \pm 0.21 \mu Jy .
The stacked emission is unresolved , with a size < 1 " , or a physical size < 8 kpc .
The total 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 star forming galaxies .
The star formation rate derived from a similar analysis of the UV luminosities is 17 M _ { \odot } year ^ { -1 } , without any correction for UV dust attenuation .
The simplest conclusion is that the dust attenuation factor is 1.8 at UV wavelengths .
However , this factor is considerably smaller than the standard attenuation factor \sim 5 , normally assumed for LBGs .
We discuss potential reasons for this discrepancy , including the possibility that the dust attenuation factor at z \geq 3 is smaller than at lower redshifts .
Conversely , the radio luminosity for a given star formation rate may be systematically lower at very high redshift .
Two possible causes for a suppressed radio luminosity are : ( i ) increased inverse Compton cooling of the relativistic electron population due to scattering off the increasing CMB at high redshift , or ( ii ) cosmic ray diffusion from systematically smaller galaxies .
The radio detections of individual sources are consistent with a radio-loud AGN fraction of 0.3 % .
One source is identified as a very dusty , extreme starburst galaxy ( a ’ submm galaxy ’ ) .