An indirect measurement of gas evolution in galaxies at $0.5\leq z \leq
  2.0$
  One key piece of information missing from high redshift galaxy surveys is the
galaxies' cold gas contents. We present a new method to indirectly determine
cold gas surface densities and integrated gas masses from galaxy star formation
rates and to separate the atomic and molecular gas components. Our predicted
molecular and total gas surface densities and integrated masses are in very
good agreement with direct measurements quoted in the literature for low and
high-z galaxies. We apply this method to predict the gas content for a sample
of $\sim 57000$ galaxies in the COSMOS field at $0.5 \leq z \leq 2.0$, selected
to have $I_{AB} < 24$ mag. This approach allows us to investigate in detail the
redshift evolution of galaxy cold and molecular gas content versus stellar mass
and to provide fitting formulae for galaxy gas fractions. We find a clear trend
between galaxy gas fraction, molecular gas fraction and stellar mass with
redshift, suggesting that massive galaxies consume and/or expel their gas at
higher redshift than less massive objects and have lower fractions of their gas
in molecular form. The characteristic stellar mass separating gas- from
stellar-dominated galaxies decreases with time. This indicates that massive
galaxies reach a gas-poor state earlier than less massive objects. These trends
can be considered to be another manifestation of downsizing in star formation
activity.
