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Neutral hydrogen (HI) will soon be the dark matter tracer observed over thelargest volumes of Universe thanks to the 21 cm intensity mapping technique. Tounveil cosmological information it is indispensable to understand the HIdistribution with respect to dark matter. Using a full one-loop derivation ofthe power spectrum of HI, we show that higher order corrections change theamplitude and shape of the power spectrum on typical cosmological (linear)scales. These effects go beyond the expected dark matter non-linear correctionsand include non-linearities in the way the HI signal traces dark matter. Weshow that, on linear scales at z = 1, the HI bias drops by up to 15% in bothreal and redshift space, which results in underpredicting the mass of the halosin which HI lies. Non-linear corrections give rise to a significant scaledependence when redshift space distortions arise, in particular on the scalerange of the baryonic acoustic oscillations (BAO). There is a factor of 5difference between the linear and full HI power spectra over the full BAO scalerange, which will modify the ratios between the peaks. This effect will also beseen in other types of survey and it will be essential to take it into accountin future experiments in order to match the expectations of precisioncosmology.

A scale dependent bias on linear scales: the case for HI intensity mapping at z=1