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In cold dark matter cosmology, the baryonic components of galaxies arethought to be mixed with and embedded in non-baryonic and non-relativistic darkmatter, 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 increaseswith disk radius, becoming appreciable and then dominant in the outer, baryonicregions of the disks of star-forming galaxies. This results in rotationvelocities of the visible matter within the disk that are constant orincreasing with disk radius. Comparison between the dynamical mass and the sumof stellar and cold gas mass at the peak epoch of galaxy formation, inferredfrom ancillary data, suggest high baryon factions in the inner, star-formingregions of the disks. Although this implied baryon fraction may be larger thanin the local Universe, the systematic uncertainties (stellar initial massfunction, calibration of gas masses) render such comparisons inconclusive interms of the mass of dark matter. Here we report rotation curves for the outerdisks of six massive star-forming galaxies, and find that the rotationvelocities are not constant, but decrease with radius. We propose that thistrend arises because of two main factors: first, a large fraction of themassive, high-redshift galaxy population was strongly baryon dominated, withdark matter playing a smaller part than in the local Universe; and second, thelarge velocity dispersion in high-redshift disks introduces a substantialpressure term that leads to a decrease in rotation velocity with increasingradius. The effect of both factors appears to increase with redshift.Qualitatively, the observations suggest that baryons in the early Universeefficiently condensed at the centres of dark matter halos when gas fractionswere high, and dark matter was less concentrated. [Abridged]

Strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago