  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.
