Extreme spheres: counts-in-cells for 21cm intensity mapping

Intensity mapping surveys will provide access to a coarse view of the cosmic large-scale structure at high redshifts. Given the large fraction of the sky that can be efficiently scanned using emission from cosmic neutral hydrogen (HI), intensity mapping is ideally suited to probe a wide range of density environments and hence to constrain cosmology and fundamental physics. To efficiently extract information from 21 cm intensities beyond average, one needs non-Gaussian statistics that capture large deviations from the mean HI density. Counts-in-cells are ideally suited for this purpose, as their statistics can be predicted accurately. We use a large state-of-the-art magnetohydrodynamic simulation from the IllustrisTNG project to determine the relation between neutral hydrogen and matter densities in cells. We demonstrate how our theoretical knowledge about the matter probability density function (PDF) for a given cosmology can be used to extract a parametrization-independent HI bias function from a measured HI PDF. Inspired by the shape of this bias function, we employ a simple quadratic approximation that reproduces the measured bias function at a few per cent level. Combining this quadratic bias function with the predicted matter PDF yields a fully predictive forward model for the HI PDF that matches the measured HI PDF at a few per cent accuracy at scale R = 5 Mpc h(-1 )from redshift z = 5 to z = 1. Furthermore, we find a density-dependent HI clustering signal that is consistent with theoretical expectations and could allow for joint constraints of HI bias and the amplitude of matter fluctuations or the growth of structure.