Molecular gas mass functions of normal star forming galaxies since z~3
  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).
