Stars form from cold molecular interstellar gas. Since this is relatively rare in the local Universe, galaxies like the Milky Way form only a few new stars per year. Typical massive galaxies in the distant Universe formed stars an order of magnitude more rapidly. Unless star formation was significantly more efficient, this difference suggests that young galaxies were much more gas rich. Molecular gas observations in the distant Universe have so far been largely restricted to very luminous, rare objects, including mergers and quasars. Here we report the results of a systematic survey of molecular gas in samples of typical massive star forming galaxies at <z>~1.2 and 2.3, when the Universe was 40% and 24% of its current age. Our measurements provide empirical evidence that distant star forming galaxies indeed were gas rich, and that the star formation efficiency is not strongly dependent on cosmic epoch. The average fraction of cold gas relative to total galaxy baryonic mass at z= 2.3 and z=1.2 is ~44% and 34%, three to ten times higher than in todays massive spiral galaxies. The slow decrease between z~2 and 1 probably requires a mechanism of semi-continuous replenishment of fresh gas to the young galaxies.
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