  We investigate the possibility that patches of old radio plasma (`radio
ghosts') of former radio galaxies form a second distinct phase of the
inter-galactic medium (IGM), not mixed with the thermal gas. The separation of
this phase from the ambient gas and its resistance against eroding turbulent
forces is given by magnetic fields, which are expected to be roughly in
pressure equilibrium with the surrounding medium. Since patches of this plasma
are largely invisible in the radio we use the term `radio ghost' to
characterize their nature. Possibilities and difficulties of different
detection strategies of ghosts are discussed. These involve radio emission,
cosmic microwave background (CMB) and starlight Comptonization, and Faraday
rotation. Re-activation of the electron population in shock waves of
cosmological structure formation, which seems to lead to the cluster radio
relic phenomena. We discuss the role radio ghosts can have: They are able to
store relativistic particles for cosmological times, but are also able to
release them under the influence of very strong turbulence. This might happen
during a major merger event of clusters of galaxies. The released relativistic
proton population could produce the observed radio halos of some cluster of
galaxies via hadronic reactions with the background gas leading to the
production of secondary electrons and positrons. Destroyed ghosts, mixed with
the IGM can help to magnetize it. Finally, the strong field strength within
ghosts should have a significant impact on the propagation of extragalactic
high energy cosmic rays.
