On the spatial distribution of neutral hydrogen in the Universe: bias and shot-noise of the H i 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 H i 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 H i over cosmic time. Motivated by this, we build an analytic framework where the relevant parameters that govern how the H i 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 H i 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 H i and the mean number density of H i 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 H i bias is relatively higher than the value reported in similar studies, but the shot noise level is always sub-dominant, making the H i power spectrum always a high signal-to-noise measurement up to z ≃ 5 in the limit of no instrumental noise and foreground contamination.