Voids in Redshift Space
  We study the ellipticity probability distribution function (PDF) of voids in
redshift space with galaxies as tracers of the shapes of voids. We find that
the redshift space distortion on the shape of voids statistically increases the
ellipticities of voids, and leaves a prominent feature on the ellipticity PDF
as a substantial reduction in the probability of having voids with small
ellipticity. The location of this characteristic cutoff of the ellipticity PDF
is an explicit function of the logarithmic growth rate, and it can be used as a
probe of cosmology once the radial density profile of voids is better
understood. However, the biggest limiting factor for the use of ellipticity PDF
as a probe of cosmology lies in the Poisson noise from a small number of
galaxies to define the shape of a given void. This Poisson noise creates a
significant contamination of the resulting ellipticity PDF so that the shape of
the original PDF is almost washed-out. Nevertheless, there is a way to overcome
the Poisson noise via the Alcock Paczynski test on the shape of stacked voids.
In redshift space, since the void is elongated toward the line of sight, the
stacked void has non-zero ellipticity, which can be a tell-tale of the
logarithmic growth rate. Although some useful information of void ellipticity
will be lost by stacking, in this way, we can see the effect of redshift space
distortion as a source of anisotropy in the stacked void ellipticity. We think
that the stacking analysis of the voids in redshift space is potentially a
powerful tool to probe the cosmology.
