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Observations show that star formation in galaxies is closely correlated withthe abundance of molecular hydrogen. Modeling this empirical relation fromfirst principles proves challenging, however, and many questions regarding itsproperties remain open. For instance, the exact functional form of the relationis still debated and it is also unknown whether it applies at z>4, where COobservations are sparse. Here, we analyze how the shape of the star formation-- gas relation affects the cosmic star formation history and global galaxyproperties using an analytic model that follows the average evolution ofgalaxies in dark matter halos across cosmic time. We show that a linearrelation with an H2 depletion time of ~2.5 Gyr, as found in studies of nearbygalaxies, results in good agreement with current observations of galaxies atboth low and high redshift. These observations include the evolution of thecosmic star formation rate density, the z~4-9 UV luminosity function, theevolution of the mass -- metallicity relation, the relation between stellar andhalo mass, and the gas-to-stellar mass ratios of galaxies. In contrast, theshort depletion times that result from adopting a highly super-linear starformation -- gas relation lead to large star formation rates, substantial metalenrichment (~0.1 solar), and low gas-to-stellar mass ratios already at z~10, indisagreement with observations. These results can be understood in terms of anequilibrium picture of galaxy evolution in which gas inflows, outflows, andstar formation drive the metallicities and gas fractions toward equilibriumvalues that are determined by the ratio of the accretion time to the gasdepletion time. In this picture, the cosmic modulation of the accretion rate isthe primary process that drives the evolution of stellar masses, gas masses,and metallicities of galaxies from high redshift until today.

Lessons from cosmic history: The case for a linear star formation -- H2 relation