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 _ { H _ { 2 } } = ( 6.8 - 8.8 ) ~ { } \times~ { } 10 ^ { 7 } ~ { } M _ { \odot } ~ { } { Mpc } ^ { -3 } at z = 1 - 1.5 and 6.7 \times 10 ^ { 6 } ~ { } M _ { \odot } ~ { } { 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 .