  In cold dark matter cosmology, the baryonic components of galaxies are
thought to be mixed with and embedded in non-baryonic and non-relativistic dark
matter, which dominates the total mass of the galaxy and its dark matter halo.
In the local Universe, the mass of dark matter within a galactic disk increases
with disk radius, becoming appreciable and then dominant in the outer, baryonic
regions of the disks of star-forming galaxies. This results in rotation
velocities of the visible matter within the disk that are constant or
increasing with disk radius. Comparison between the dynamical mass and the sum
of stellar and cold gas mass at the peak epoch of galaxy formation, inferred
from ancillary data, suggest high baryon factions in the inner, star-forming
regions of the disks. Although this implied baryon fraction may be larger than
in the local Universe, the systematic uncertainties (stellar initial mass
function, calibration of gas masses) render such comparisons inconclusive in
terms of the mass of dark matter. Here we report rotation curves for the outer
disks of six massive star-forming galaxies, and find that the rotation
velocities are not constant, but decrease with radius. We propose that this
trend arises because of two main factors: first, a large fraction of the
massive, high-redshift galaxy population was strongly baryon dominated, with
dark matter playing a smaller part than in the local Universe; and second, the
large velocity dispersion in high-redshift disks introduces a substantial
pressure term that leads to a decrease in rotation velocity with increasing
radius. The effect of both factors appears to increase with redshift.
Qualitatively, the observations suggest that baryons in the early Universe
efficiently condensed at the centres of dark matter halos when gas fractions
were high, and dark matter was less concentrated. [Abridged]
