  It has recently been shown that the abundance of cold neutral gas may follow
a similar evolution as the star formation history. This is physically
motivated, since stars form out of this component of the neutral gas and if the
case, would resolve the longstanding issue that there is a clear disparity
between the total abundance of neutral gas and star forming activity over the
history of the Universe. Radio-band 21-cm absorption traces the cold gas and
comparison with the Lyman-alpha absorption, which traces all of the gas,
provides a measure of the cold gas fraction or the spin temperature. The recent
study has shown that the spin temperature (degenerate with the ratio of the
absorber/emitter extent) appears to be anti-correlated with the star formation
density, undergoing a similar steep evolution as the star formation rate over
redshifts of 0 < z < 3, whereas the total neutral hydrogen exhibits little
evolution. Above z > 3, where the SFR shows a steep decline with redshift,
there is insufficient 21-cm data to determine whether the spin temperature
continues to follow the SFR. Knowing this is paramount in ascertaining whether
the cold neutral gas does trace the star formation over the Universe's history.
We explore the feasibility of resolving this with 21-cm observations of the
largest contemporary sample of reliable damped Lyman-alpha absorption systems
and conclude that, while today's largest radio interferometers can reach the
required sensitivity at z < 3.5, the Square Kilometre Array is required to
probe to higher redshifts.
