Fast Transients at Cosmological Distances with the SKA
  Impulsive radio bursts that are detectable across cosmological distances
constitute extremely powerful probes of the ionized Inter-Galactic Medium
(IGM), intergalactic magnetic fields, and the properties of space-time itself.
Their dispersion measures (DMs) will enable us to detect the "missing" baryons
in the low-redshift Universe and make the first measurements of the mean galaxy
halo profile, a key parameter in models of galaxy formation and feedback.
Impulsive bursts can be used as cosmic rulers at redshifts exceeding 2, and
constrain the dark energy equation-of-state parameter, $w(z)$ at redshifts
beyond those readily accessible by Type Ia SNe. Both of these goals are
realisable with a sample of $\sim 10^4$ fast radio bursts (FRBs) whose
positions are localized to within one arcsecond, sufficient to obtain host
galaxy redshifts via optical follow-up. It is also hypothesised that
gravitational wave events may emit coherent emission at frequencies probed by
SKA1-LOW, and the localization of such events at cosmological distances would
enable their use as cosmological standard sirens.
  To perform this science, such bursts must be localized to their specific host
galaxies so that their redshifts may be obtained and compared against their
dispersion measures, rotation measures, and scattering properties. The SKA can
achieve this with a design that has a wide field-of-view, a substantial
fraction of its collecting area in a compact configuration (80\% within a 3\,km
radius), and a capacity to attach high-time-resolution instrumentation to its
signal path.
