  Neutral hydrogen (HI) will soon be the dark matter tracer observed over the
largest volumes of Universe thanks to the 21 cm intensity mapping technique. To
unveil cosmological information it is indispensable to understand the HI
distribution with respect to dark matter. Using a full one-loop derivation of
the power spectrum of HI, we show that higher order corrections change the
amplitude and shape of the power spectrum on typical cosmological (linear)
scales. These effects go beyond the expected dark matter non-linear corrections
and include non-linearities in the way the HI signal traces dark matter. We
show that, on linear scales at z = 1, the HI bias drops by up to 15% in both
real and redshift space, which results in underpredicting the mass of the halos
in which HI lies. Non-linear corrections give rise to a significant scale
dependence when redshift space distortions arise, in particular on the scale
range of the baryonic acoustic oscillations (BAO). There is a factor of 5
difference between the linear and full HI power spectra over the full BAO scale
range, which will modify the ratios between the peaks. This effect will also be
seen in other types of survey and it will be essential to take it into account
in future experiments in order to match the expectations of precision
cosmology.
