  (Abridged) We investigate the spectral distortion of the cosmic microwave
background (CMB) caused by relativistic plasma. Within the Thomson regime, an
exact analytic expression for the photon scattering kernel of a momentum
power-law electron distribution is given. The ultra-relativistic
Sunyaev-Zeldovich (SZ) decrement measures the electron number and not the
energy content. On the other hand, the relativistic SZ increment at higher
frequencies depends strongly on the spectral shape of the electrons. We
calculate the expected Comptonization due to the energy release of radio
galaxies, which we estimate to be 3 10^66 erg Gpc^-3. We investigate
Comptonization from (a) the part of the released energy which is thermalized
and (b) the relativistic, remnant radio plasma, which may form a second,
relativistic phase in the inter galactic medium, nearly unobservable for
present day instruments (presence of so called 'radio ghosts'). We find a
thermal Comptonization parameter due to (a) of y = 10^-6 and (b) an optical
depth of relativistic electrons in old radio plasma of tau_rel < 10^-7. If a
substantial fraction of the volume of clusters of galaxies is filled with such
old radio plasma the SZ effect based determination of the Hubble constant is
biased to lower values. Finally, it is shown that a supra-thermal population of
electrons in the Coma cluster would produce a signature in the Wien-tail of the
CMB, which is marginally detectable with a multifrequency measurement by the
Planck satellite. Such a population is expected to exist, since its
bremsstrahlung would explain Coma's recently reported high energy X-ray excess.
