Void Ellipticity Distribution as a Probe of Cosmology

Cosmic voids refer to the large empty regions in the Universe with a very low number density of galaxies. Voids are likely to be severely disturbed by the tidal effect from the surrounding dark matter. We derive a completely analytic model for the void ellipticity distribution from physical principles. We use the spatial distribution of galaxies in a void as a measure of its shape, tracking the trajectory of the void galaxies under the influence of the tidal field using Lagrangian perturbation theory. Our model implies that the void ellipticity distribution depends sensitively on the cosmological parameters. Testing our model against the high-resolution Millennium Run simulation, we find excellent quantitative agreements of the analytic predictions with the numerical results.