Though observationally rare , damped Ly \alpha absorption systems dominate the mass density of neutral gas in the Universe . Eleven high redshift damped Ly \alpha 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 \sim 2 as indicated by previous studies . There is evidence in the observed \Omega _ { g } for a flattening at z \sim 2 and a possible turnover at z \sim 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 } \geq 21 atoms cm ^ { -2 } , these results point to an epoch at z _ { > } \atop { { } ^ { \sim } } 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 , i.e . 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 found that \Omega ( z \approx 3.5 ) was twice \Omega ( z \approx 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 .