On the spatial distribution of neutral hydrogen in the Universe: Bias and shot-noise of the HI power spectrum

The spatial distribution of neutral hydrogen (H I) in the Universe contains a wealth of cosmological information. The 21-cm emission line can be used to map the HI up to very high redshift and therefore reveal us something about the evolution of the large-scale structures in the Universe. However, little is known about the abundance and clustering properties of the HI over cosmic time. Motivated by this, we build an analytic framework where the relevant parameters that govern how the HI is distributed among dark matter haloes can be fixed using observations. At the same time, we provide tools to study the column density distribution function of the HI absorbers together with their clustering properties. Our formalism is the first one able to account for all observations at a single redshift, z = 2.3. The linear bias of the HI and the mean number density of HI sources, two main ingredients in the calculation of the signal-to-noise ratio of a cosmological survey, are then discussed in detail, also extrapolating the results to low and high redshift. We find that HI bias is relatively higher than the value reported in similar studies, but the shot noise level is always sub-dominant, making the HI power spectrum always a high signal-to-noise measurement up to z ≃ 5 in the limit of no instrumental noise and foreground contamination.