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 (HI) 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 halos 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 measurements up to $z\simeq5$ in the limit of no
instrumental noise and foreground contamination.
