The results of a new spectroscopic survey of 66 $z simgt 4$ quasars for Damped Lyman-alpha absorption systems are presented. The search led to the discovery of 30 new DLA candidates which are analysed in order to compute the comoving mass density of neutral gas in a non-zero lambda Universe. The possible sources of uncertainty are discussed and the implications of our results for the theories of galaxy formation and evolution are emphasized. A subsequent paper will present details of the calculations summarised here and a more extensive explanation of the consequences of our observations for the understanding of the nature of DLAs.
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