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.