Cosmic Voids and Galaxy Bias in the Halo Occupation Framework

(Abridged) We investigate the power of void statistics to constrain galaxy bias and the amplitude of dark matter fluctuations. We use the halo occupation distribution (HOD) framework to describe the relation between galaxies and dark matter. After choosing HOD parameters that reproduce the mean space density ngal and projected correlation function wₚ measured for galaxy samples with Mᵣ<-19 and Mᵣ<-21 from the Sloan Digital Sky Survey (SDSS), we predict the void probability function (VPF) and underdensity probability function (UPF) of these samples by populating the halos of a large, high-resolution N-body simulation. If we make the conventional assumption that the HOD is independent of large scale environment at fixed halo mass, then models constrained to match ngal and wₚ predict nearly identical void statistics, independent of the scatter between halo mass and central galaxy luminosity or uncertainties in HOD parameters. Models with sigma₈=0. 7 and sigma₈=0. 9 also predict very similar void statistics. However, the VPF and UPF are sensitive to environmental variations of the HOD in a regime where these variations have little impact on wₚ. For example, doubling the minimum host halo mass in regions with large scale (5 Mpc/h) density contrast delta<-0. 65 has a readily detectable impact on void probabilities of Mᵣ<-19 galaxies, and a similar change for delta<-0. 2 alters the void probabilities of Mᵣ<-21 galaxies at a detectable level. The VPF and UPF provide complementary information about the onset and magnitude of density- dependence in the HOD. By detecting or ruling out HOD changes in low density regions, void statistics can reduce systematic uncertainties in the cosmological constraints derived from HOD modeling, and, more importantly, reveal connections between halo formation history and galaxy properties.