Temporal Smearing of Transient Radio Sources by the Intergalactic Medium
  The temporal smearing of impulsive radio events at cosmological redshifts
probes the properties of the ionized Inter-Galactic Medium (IGM). We relate the
degree of temporal smearing and the profile of a scattered source to the
evolution of turbulent structure in the IGM as a function of redshift. We
estimate the degree of scattering expected by analysing the contributions to
the Scattering Measure (SM) of the various components of baryonic matter
embedded in the IGM, including the diffuse IGM, intervening galaxies and
intracluster gas. These estimates predict that the amount of temporal smearing
expected at 300\,MHz is typically as low as ~1 ms and suggests that these
bursts may be detectable with low frequency widefield arrays. A generalization
of the DM-SM relation observed for Galactic scattering to the densities and
turbulent conditions relevant to the IGM suggests that scattering measures of
order 10^{-6} kpc m {-20/3} would be expected at z ~ 1. This scattering is
sufficiently low that its effects would, for most lines of sight, not be
manifest in existing observations of the scattering broadening in images of
extragalactic compact sources. The redshift dependence of the temporal smearing
discriminates between scattering that occurs in the host galaxy of the burst
and the IGM, with tau_host \propto (1+z)^{-3} if the scattering probes length
scales below the inner scale of the turbulence or tau_host \propto
(1+z)^{-17/5} if the turbulence follows a Kolmogorov spectrum. This differs
strongly from the expected IGM scaling tau_{IGM} ~ z^2 for z < 1 and
(1+z)^{0.2-0.5} for z >> 1.
