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Recently the EDGES experiment has claimed the detection of an absorptionfeature centered at 78 MHz. When interpreted as a signature of cosmic dawn,this feature appears at the correct wavelength (corresponding to a redshiftrange of $z\approx15-20$) but is larger by at least a factor of two inamplitude compared to the standard 21-cm models. One way to explain the excessradio absorption is by the enhancement of the diffuse radio background at $\nu= 1.42$ GHz ($\lambda=21$ cm) in the rest frame of the absorbing neutralhydrogen. Astrophysical scenarios, based on the acceleration of relativisticelectrons by accretion on to supermassive black holes (SMBHs) and by supernovae(SN) from first stars, have been proposed to produce the enhanced radiobackground via synchrotron emission. In this Letter we show that either thesynchrotron or the inverse-Compton (IC) cooling time for such electrons is atleast three orders of magnitude shorter than the duration of the EDGES signalcentered at $z \approx 17$, irrespective of the magnetic field strength. Thesynchrotron radio emission at 1.42 GHz due to rapidly cooling electrons is$\sim 10^3$ times smaller than the non-cooling estimate. Thus astrophysicalscenarios for excess radio background proposed to explain the EDGES signalappear very unlikely.

Astrophysical radio background cannot explain the EDGES 21-cm signal: constraints from cooling of non-thermal electrons