The evolution of the baryons associated with galaxies averaged over cosmic time and space

We combine the recent determination of the evolution of the cosmic density of molecular gas (H2) using deep, volumetric surveys, with previous estimates of the cosmic density of stellar mass, star formation rate and atomic gas (H I), to constrain the evolution of baryons associated with galaxies averaged over cosmic time and space. The cosmic H I and H2 densities are roughly equal at z ~ 1.5. The H2 density then decreases by a factor 6+3-2 to today's value, whereas the H I density stays approximately constant. The stellar mass density is increasing continuously with time and surpasses that of the total gas density (H I and H2) at redshift z ~ 1.5. The growth in stellar mass cannot be accounted for by the decrease in cosmic H2 density, necessitating significant accretion of additional gas onto galaxies. With the new H2 constraints, we postulate and put observational constraints on a two-step gas accretion process: (i) a net infall of ionized gas from the intergalactic/circumgalactic medium to refuel the extended H I reservoirs, and (ii) a net inflow of H I and subsequent conversion to H2 in the galaxy centers. Both the infall and inflow rate densities have decreased by almost an order of magnitude since z ~ 2. Assuming that the current trends continue, the cosmic molecular gas density will further decrease by about a factor of two over the next 5 Gyr, the stellar mass will increase by approximately 10%, and cosmic star formation activity will decline steadily toward zero, as the gas infall and accretion shut down.