Evolution of Cosmic Molecular Gas Mass Density From z ~ 0 to z = 1 -1.5

We try to constrain the cosmic molecular gas mass density at $z =1-1.5$ and that in the local universe by combining stellar mass functions of star-forming galaxies and their average molecular gas mass fractions against the stellar mass. The average molecular gas mass fractions are taken from recent CO observations of star-forming galaxies at the redshifts. The cosmic molecular gas mass density is obtained to be $\rho_{\rm H_2} = (6.8-8.8)~\times~10^7~M_\odot~{\rm Mpc}^{-3}$ at $z=1-1.5$ and $6.7 \times 10^6~M_\odot~{\rm Mpc}^{-3}$ at $z \sim 0$ by integrating down to $0.03~M^\ast$. Although the values have various uncertainties, the cosmic molecular gas mass density at $z =1-1.5$ is about ten times larger than that in the local universe. The cosmic star formation rate density at $z \sim 1-2$ is also about ten times larger than that in the local universe. Our result suggests that the large cosmic molecular gas mass density at $z=1-1.5$ accounts for the large cosmic star formation rate density at $z \sim 1 -2$.