A., Biermann P

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.