Fluctuations in the radio background from intergalactic synchrotron emission

The shocks produced in the intergalactic medium during large-scale structure formation accelerate a population of highly relativistic electrons that emit synchrotron radiation due to intergalactic magnetic fields. In a previous paper we have shown that these electrons cool primarily by inverse Compton scattering of the microwave background photons and can thereby produce the observed intensity and spectrum of the diffuse gamma -ray background. Here we calculate the intensity and angular fluctuations of the radio synchrotron background that results from the same high-energy electrons as well as the expected angular fluctuations in the gamma -ray background. On angular scales smaller than a degree, the predicted fluctuations in the microwave background temperature are of order 40 muK(xi (B)/0.01)(nu /10 GHz)(-3), where xi (B) is the magnetic fraction of the postshock energy density. This foreground might have already dominated the anisotropy signal detected in existing low-frequency cosmic microwave background experiments and can be identified with confidence through multifrequency observations. Detection of the synchrotron fluctuations would allow us to determine the strength of the intergalactic magnetic field. We predict a strong correlation between high-resolution maps taken at low-frequency radio waves and at high-energy gamma -rays. Young X-ray clusters may also appear as radio or gamma -ray clusters. The detailed study of this correlation will become easily accessible with the future launch of the Gamma-Ray Large-Area Space Telescope.