Observations show that star formation in galaxies is closely correlated with the abundance of molecular hydrogen . Modeling this empirical relation from first principles proves challenging , however , and many questions regarding its properties remain open . For instance , the exact functional form of the relation is still debated and it is also unknown whether it applies at z > 4 , where { CO } observations are sparse . Here , we analyze how the shape of the star formation – gas relation affects the cosmic star formation history and global galaxy properties using an analytic model that follows the average evolution of galaxies in dark matter halos across cosmic time . We show that a linear relation with an { { H } _ { 2 } } depletion time of \sim { } 2.5 Gyr , as found in studies of nearby galaxies , results in good agreement with current observations of galaxies at both low and high redshift . These observations include the evolution of the cosmic star formation rate density , the z \sim { } 4 - 9 UV luminosity function , the evolution of the mass – metallicity relation , the relation between stellar and halo mass , and the gas-to-stellar mass ratios of galaxies . In contrast , the short depletion times that result from adopting a highly super-linear star formation – gas relation lead to large star formation rates , substantial metal enrichment ( \sim { } 0.1 Z _ { \odot } ) , and low gas-to-stellar mass ratios already at z \gtrsim { } 10 , in disagreement with observations . These results can be understood in terms of an equilibrium picture of galaxy evolution in which gas inflows , outflows , and star formation drive the metallicities and gas fractions toward equilibrium values that are determined by the ratio of the accretion time to the gas depletion time . In this picture , the cosmic modulation of the accretion rate is the primary process that drives the evolution of stellar masses , gas masses , and metallicities of galaxies from high redshift until today .