  The clustering pattern in high redshift HI maps is expected to be anisotropic
due to two distinct reasons, the
  Alcock-Paczynski effect and the peculiar velocities, both of which are
sensitive to the cosmological parameters. The signal is also expected to be
sensitive to the details of the HI distribution at the epoch when the radiation
originated. We use simple models for the HI distribution at the epoch of
reionizaation and the post-reionization era to investigate exactly what we hope
to learn from future observations of the anisotropy pattern in HI maps. We find
that such observations will probably tell us more about the HI distribution
than about the background cosmological model. Assuming that reionization can be
described by spherical, ionized bubbles all of the same size with their centers
possibly being biased with respect to the dark matter, we find that the
anisotropy pattern at small angles is expected to have a bump at the
characteristic angular size of the individual bubbles whereas the large scale
anisotropy pattern will reflect the size and the bias of the bubbles. The
anisotropy also depends on the background cosmological parameters, but the
dependence is much weaker. Under the assumption that the HI in the
post-reionization era traces the dark matter with a possible bias, we find that
changing the bias and changing the background cosmology has similar effects on
the anisotropy pattern. Combining observations of the anisotropy with
independent estimates of the bias, possibly from the bi-spectrum, may allow
these observations to constrain cosmological parameters.
