  We combine the galaxy formation model GALFORM with the Photon Dominated
Region code UCL_PDR to study the emission from the rotational transitions of
12CO (CO) in galaxies from z=0 to z=6 in the Lambda CDM framework. GALFORM is
used to predict the molecular (H2) and atomic hydrogen (HI) gas contents of
galaxies using the pressure-based empirical star formation relation of Blitz &
Rosolowsky. From the predicted H2 mass and the conditions in the interstellar
medium, we estimate the CO emission in the rotational transitions 1-0 to 10-9
by applying the UCL_PDR model to each galaxy. We find that deviations from the
Milky-Way CO-H2 conversion factor come mainly from variations in metallicity,
and in the average gas and star formation rate surface densities. In the local
universe, the model predicts a CO(1-0) luminosity function (LF), CO-to-total
infrared (IR) luminosity ratios for multiple CO lines and a CO spectral line
energy distribution (SLED) which are in good agreement with observations of
luminous and ultra-luminous IR galaxies. At high redshifts, the predicted CO
SLED of the brightest IR galaxies reproduces the shape and normalization of the
observed CO SLED. The model predicts little evolution in the CO-to-IR
luminosity ratio for different CO transitions, in good agreement with
observations up to z~5. We use this new hybrid model to explore the potential
of using colour selected samples of high-redshift star-forming galaxies to
characterise the evolution of the cold gas mass in galaxies through
observations with the Atacama Large Millimeter Array.
