There is a well known disparity between the evolution the star formation rate density, {psi}*, and the abundance of neutral hydrogen (HI), the raw material for star formation. Recently, however, we have shown that {psi}* may be correlated with the fraction of cool atomic gas, as traced through the 21-cm absorption of HI. This is expected since star formation requires cold (T ~ 10 K) gas and so this could address the issue of why the star formation rate density does not trace the bulk atomic gas. The data are, however, limited to redshifts of z < 2, where both {psi}* and the cold gas fraction exhibit a similar steep climb from the present day (z = 0), and so it is unknown whether the cold gas fraction follows the same decline as {psi}* at higher redshift. In order to address this, we have used unpublished archival observations of 21-cm absorption in high redshift damped Lyman-{alpha} absorption systems to increase the sample at z > 2. The data suggest that the cold gas fraction does exhibit a decrease, although this is significantly steeper than {psi}* at z ~ 3. This is, however, degenerate with the extents of the absorbing galaxy and the background continuum emission and upon removing these, via canonical evolution models, we find the mean spin temperature of the gas to be <T> ~ 3000 K, compared to the ~2000 K expected from the fit at z < 2. These temperatures are consistent with the observed high neutral hydrogen column densities, which require T < 4000 K in order for the gas not to be highly ionised.
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