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Radio observations of Gamma Ray Bursts afterglows are fundamental inproviding insights into their physics and environment, and in constraining thetrue energetics of these sources. Nonetheless, radio observations of GRBafterglows are presently sparse in the time/frequency domain. Starting from acomplete sample of 58 bright Swift long bursts (BAT6), we constructed ahomogeneous sub-sample of 38 radio detections/upper limits which preserves allthe properties of the parent sample. One half of the bursts have detectionsbetween 1 and 5 days after the explosion with typical fluxes F>100 muJy at 8.4GHz. Through a Population SYnthesis Code coupled with the standard afterglowHydrodynamical Emission model (PSYCHE) we reproduce the radio flux distributionof the radio sub-sample. Based on these results we study the detectability inthe time/frequency domain of the entire long GRB population by present andfuture radio facilities. We find that the GRBs that typically trigger Swift canbe detected at 8.4 GHz by JVLA within few days with modest exposures even athigh redshifts. The final SKA can potentially observe the whole GRB populationprovided that there will be a dedicated GRB gamma-ray detector more sensitivethan Swift. For a sizable fraction (50%) of these bursts, SKA will allow us toperform radio-calorimetry, after the trans-relativistic transition (occurring~100 d), providing an estimate of the true (collimation corrected) energeticsof GRBs.

Radio afterglows of a complete sample of bright Swift GRBs: predictions from present days to the SKA era