The geometry effects of an expanding Universe on the detection of cool neutral gas at high redshift

Recent high redshift surveys for 21-cm absorption in damped Lyman-alpha absorption systems (DLAs) take the number of published searches at z > 2 to 25, the same number as at z < 2, although the detection rate at high redshift remains significantly lower (20% cf. 60%). Using the known properties of the DLAs to estimate the unknown profile widths of the 21-cm non-detections and including the limits via a survival analysis, we show that the mean spin temperature/covering factor degeneracy at high redshift is, on average, double that of the low redshift sample. This value is significantly lower than the previous factor of eight for the spin temperatures and is about the same factor as in the angular diameter distance ratios between the low and high redshift samples. That is, without the need for the several pivotal assumptions, which lead to an evolution in the spin temperature, we show that the observed distribution of 21-cm detections in DLAs can be accounted for by the geometry effects of an expanding Universe. That is, as yet there is no evidence of the spin temperature of gas rich galaxies evolving with redshift.