  We present evidence for the existence of shock waves caused by the formation
of the large-scale structure. In some clusters of galaxies peripherally located
sources of extended diffuse radio emission exist, the so-called cluster radio
relics. They have steep radio spectra but no apparent cutoff, as old remnants
of radio galaxies usually have. Therefore particle acceleration has to take
place within them. We propose that shock structures of the cosmological
large-scale matter flows are responsible for the acceleration of relativistic
electrons: cluster accretion shocks and bow shocks of merger events. We develop
a theory of radio plasma having traversed these shocks and compare it to
observational data of nine radio relics (0038-096, 0917+75, 1140+203, 1253+275,
1712+64, 1706+78, 2006-56, 2010-57, 1401-33) and their host clusters (A85,
A786, A1367, Coma, A2255, A2256, A3667, S753). The necessary accretion power,
the spectral index of the radio spectrum, the acceleration efficiency of the
shock, the diffusion coefficient in the post-shock region, and the predicted
radio polarization in all of our examples fit into a coherent interpretation of
the observational data. Since polarization measurements are available only for
four sources, the predictions of our theory can be independently checked using
other examples. The predicted values of the shock compression ratio, density
and temperature of the infalling gas, magnetic field strength of the shocked
and unshocked radio plasma are discussed within the frame of structure
formation theory.
