The statistics of voids as a tool to constrain cosmological parameters: sigma_8 and Omega_m h

TL;DR

This paper develops an analytical framework to analyze void statistics in the universe, enabling constraints on cosmological parameters like sigma_8 and Omega_m h from galaxy surveys.

Contribution

The paper introduces a new formalism for accurately calculating void statistics in galaxy distributions, linking them to cosmological parameters and observational effects.

Findings

Void statistics are weakly dependent on redshift.

Void counts are sensitive to sigma_8 and Omega_m h.

Method allows independent cosmological parameter estimation.

Abstract

We present a general analytical formalism to calculate accurately several statistics related to underdense regions in the Universe. The statistics are computed for dark matter halo and galaxy distributions both in real space and redshift space at any redshift. Using this formalism, we found that void statistics for galaxy distributions can be obtained, to a very good approximation, assuming galaxies to have the same clustering properties as halos above a certain mass. We deducted a relationship between this mass and that of halos with the same accumulated number density as the galaxies. We also found that the dependence of void statistics on redshift is small. For instance, the number of voids larger than 13 Mpc/h (defined to not contain galaxies brighter than M_r=-20.4 +5logh change less than 20% between z=1 and z=0. However, the dependence of void statistics on sigma_8 and Omega_m h is considerably larger, making them appropriate to develop tests to measure these parameters. We have shown how to efficiently construct several of these tests and discussed in detail the treatment of several observational effects. The formalism presented here along with the observed statistics extracted from current and future large galaxy redshift surveys will provide an independent measurement of the relevant cosmological parameters. Combining these measurements with those found using other methods will contribute to reduce their uncertainties.