  Recent measurements of gas velocity in the outer parts of high redshift
galaxies suggest that steeply falling rotation curves may be common, or even
universal, in these galaxies, in contrast to the near universal flat,
non-declining rotation curves in nearby galaxies. We investigate the
implications of these postulated steeply falling rotation curves for the role
of dark matter in galaxy formation. Using an established computer code, the
collapse of dark matter and baryonic matter together, starting with a variety
of initial conditions, is simulated for comparison with the observed rotation
curves. As soon as a smooth stellar disc is formed in the baryonic matter, with
properties similar to the observed high redshift galaxies, the computed
rotation curves are, without exception, relatively flat to large radius in the
gas disc. Only a simulation without a dark matter halo is able to reproduce the
observed rotation curves. This would imply that, if the high redshift steeply
falling rotation curves turn out to be common, then the standard scenario for
galaxy formation for these galaxies, namely baryonic matter falling into the
potential well of a massive dark matter halo, must be wrong, unless there is
pressure support via velocity dispersion significantly higher than has so far
been observed. It would also imply that for these galaxies the flat rotation
curves at low redshift must be due to dark matter which has subsequently fallen
into the galactic potential well, or there must be some other explanation for
the contemporary flat rotation curves, other than dark matter.
