  Strong intergalactic shocks are a natural consequence of structure formation
in the universe. These shocks are expected to deposit large fractions of their
energy in relativistic electrons (xi_e~0.05 of the thermal energy according to
supernova remnant observations) and magnetic fields (xi_B~0.01 according to
cluster halo observations). We discuss the expected synchrotron emission from
such shocks, and the observational consequences for next generation radio
telescopes such as the Square Kilometer Array. We present an analytical model,
calibrated and verified based on a hydrodynamical LCDM simulation. The
resulting signal composes a large fraction (up to a few 10%) of the
extragalactic radio background below 500 MHz. The associated angular
fluctuations, e.g. delta T_l>260(xi_e*xi_B/5*10^-4)(nu/100 MHz)^-3 K for
multipoles 400<l<2000, dominate the radio sky for frequencies<10 GHz and
angular scales 1 arcmin-1 deg (after a modest removal of point sources),
provided that xi_e*xi_B>3*10^-4. The fluctuating signal is most pronounced for
nu<500 MHz, dominating the sky there even for xi_e*xi_B=5*10^-5. We find that
the signal is easily observable by next generation telescopes such as the SKA,
and marginally observable with present telescopes. The signal may be identified
using cross-correlations with tracers of large-scale structure (e.g. gamma-ray
emission from intergalactic shocks). Detection of the signal will provide the
first identification of intergalactic shocks and of the warm-hot intergalactic
medium (believed to contain most of the baryons in the low redshift universe),
and gauge the unknown intergalactic magnetic field.
