  There is accumulating observational evidence suggesting that damped
Ly$\alpha$ absorption systems systems are the progenitors of present-day spiral
galaxies. We use the observed properties of these systems to place constraints
on the history of star formation in galactic disks, and on cosmological
theories of structure formation in the universe. We show that the observed
increase in $\Omega_{HI}$ contributed by damped Ly$\alpha$ systems at high
redshift implies that star formation must have been considerably less efficient
in the past. We also show that the data can constrain cosmological models in
which structure forms at late epochs. A mixed dark matter (MDM) model with
$\Omega_{\nu}=0.3$ is unable to reproduce the mass densities of cold gas seen
at high redshift, even in the absence of any star formation. We show that at
redshifts greater than 3, this model predicts that the total baryonic mass
contained in dark matter halos with circular velocities $V_c > 35$ km s$^{-1}$
is less than the observed mass of HI in damped systems. At these redshifts, the
photo-ionizing background would prevent gas from dissipating and collapsing to
form high column density systems in halos smaller than 35 km s$^{-1}$. MDM
models are thus ruled out by the observations.
