Can HI gas trace the matter density distribution linearly on large scales

It is customary to assume that HI gas traces the matter density distribution linearly on large scales. However, nonlinear effects which modulate HI gas in halos might spoil this. We employ three approaches to generate the mock HI density from an N-body simulation at low redshifts, and demonstrate, for the first time, that the HI linearity assumption breaks down at $k>0.1 h\,{\rm Mpc}^{-1}$, generically, except for a "sweet-spot" redshift near $z=1.2$. In addition, the HI bias scales approximately linearly with redshift for $z\le 3$. Our findings are independent of models.