  High resolution X-ray imaging offers a unique opportunity to probe the nature
of dust in the z ~< 2 universe. Dust grains 0.1- 1 um in size will scatter soft
X-rays, producing a diffuse "halo" image around an X-ray point source, with a
brightness ~ few % confined to an arcminute-sized region. We derive the
formulae for scattering in a cosmological context and calculate the surface
brightness of the scattering halo due to (i) an IGM uniformly enriched (Omega_
d ~ 10^-5) by a power-law distribution of grain sizes, and (ii) a DLA-type (N_H
~ 10^21 cm^-2) dust screen at cosmological distances. The morphology of the
surface brightness profile can distinguish between the two scenarios above,
place size constraints on dusty clumps, and constrain the homogeneity of the
IGM. Thus X-ray scattering can gauge the relative contribution of the first
stars, dwarf galaxies, and galactic outflows to the cosmic metallicity budget
and cosmic history of dust. We show that, because the amount of intergalactic
scattering is overestimated for photon energies < 1 keV, the non-detection of
an X-ray scattering halo by Petric et al. (2006) is consistent with `grey'
intergalactic dust grains (Omega_d ~ 10^-5$) when the data is restricted to the
1-8 keV band. We also calculate the systematic offset in magnitude, delta m ~
0.01, for such a population of graphite grains, which would affect the type of
supernova survey ideal for measuring dark energy parameters within ~ 1%
precision.
