Though observationally rare, damped Lya absorption systems dominate the mass density of neutral gas in the Universe. Eleven high redshift damped Lya systems covering 2.8<z<4.4 were discovered in 26 QSOs from the APM z>4 QSO Survey, extending these absorption system surveys to the highest redshifts currently possible. Combining our new data set with previous surveys we find that the cosmological mass density in neutral gas, omega_g, does not rise as steeply prior to z~2 as indicated by previous studies. There is evidence in the observed omega_g for a flattening at z~2 and a possible turnover at z~3. When combined with the decline at z>3.5 in number density per unit redshift of damped systems with column densities log N(HI)>21 atoms cm^-2, these results point to an epoch at z>3 prior to which the highest column density damped systems are still forming. We find that over the redshift range 2<z<4 the total mass in neutral gas is marginally comparable with the total visible mass in stars in present day galaxies. However, if one considers the total mass visible in stellar disks alone, ie excluding galactic bulges, the two values are comparable. We are observing a mass of neutral gas comparable to the mass of visible disk stars. Lanzetta, Wolfe & Turnshek (1995) found that omega_g(z~3.5) was twice omega_g(z~2), implying a much larger amount of star formation must have taken place between z=3.5 and z=2 than is indicated by metallicity studies. This created a `cosmic G-dwarf problem. The more gradual evolution of omega_g we find alleviates this. These results have profound implications for theories of galaxy formation.
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