We use deep far-infrared data from the PEP/GOODS-Herschel surveys and rest frame ultraviolet photometry to study the evolution of the molecular gas mass function of normal star forming galaxies. Computing the molecular gas mass, M(mol), by scaling star formation rates (SFR) through depletion timescales, or combining IR luminosity and obscuration properties as in Nordon et al., we obtain M(mol) for roughly 700, z=0.2-3.0 galaxies near the star forming main sequence. The number density of galaxies follows a Schechter function of M(mol). The characteristic mass M* is found to strongly evolve up to z~1, and then to flatten at earlier epochs, resembling the infrared luminosity evolution of similar objects. At z~1, our result is supported by an estimate based on the stellar mass function of star forming galaxies and gas fraction scalings from the PHIBSS survey. We compare our measurements to results from current models, finding better agreement with those that are treating star formation laws directly rather than in post-processing. Integrating the mass function, we study the evolution of the M(mol) density and its density parameter Omega(mol).
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