Spectroscopic observations of distant quasars have resulted in the detection of molecular hydrogen in intervening damped Lyman-alpha absorption clouds (DLAs). We use observations compiled from different experimental groups to show that the molecular hydrogen abundance exhibits a dramatic increase over a cosmological time period corresponding to 13% to 24% of the age of the universe. We also tentatively show that the heavy element abundances in the same gas clouds exhibit a faster and more well-defined cosmological evolution compared to the general DLA population over the same time baseline. We argue that this latter point is unsurprising, because the general DLA population arises in a wide variety of galaxy types and environments, and thus a spans broad range of ISM gas-phases and abundances at the same cosmic time. DLAs exhibiting H2 absorption may therefore circumvent this problem, efficiently identifying a narrower class of objects, and provide a more sensitive probe of cosmological chemical evolution.
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