Multi-probe cosmology forecasts from HOD-based forward modeling of galaxy and void statistics

The large under-dense regions in the cosmological matter density field, known as cosmic voids, are powerful probes of cosmology but their potential is currently under-exploited. Observationally, voids are identified within the large scale distribution of galaxies and are therefore sensitive to certain features of the galaxy-halo connection. This sensitivity makes the combination of void and galaxy summary statistics particularly powerful probes of both cosmology and the galaxy-halo connection through self-calibration of the void-galaxy relation. In particular the combination of void and galaxy summary statistics breaks degeneracies in the galaxy-halo connection and cosmology relative to the case of galaxy clustering alone. To demonstrate this we forecast cosmological constraints attainable from the combination of the void size function $n_v$, projected void-galaxy cross-correlation function $w_{p,vg}$ and projected galaxy auto-correlation function $w_{p,gg}$ measured in Dark Energy Spectroscopic Instrument (DESI) Year 5 data. We use a grid of cosmological N-body simulations to model this datavector as a function of $\sigma_8$, $\Omega_m$ and a flexible halo occupation distribution (HOD) model that includes central and satellite galaxy assembly bias. For our fiducial scenario combining $n_v$, $w_{p,vg}$ and $w_{p,gg}$ we forecast $1.5\%$ and $0.8\%$ constraints on $\Omega_m$ and $\sigma_8$ from DESI-Y5 data. We also forecast constraints from the combination of the void size function and stacked weak lensing signal of voids.