Can the faint submillimetre galaxies be explained in the Λ cold dark matter model?

We present predictions for the abundance of submillimetre galaxies (SMGs) and Lyman-break galaxies (LBGs) in the cold dark matter cosmology. A key feature of our model is the self-consistent calculation of the absorption and emission of radiation by dust. The new model successfully matches the LBG luminosity function, as well as reproducing the properties of the local galaxy population in the optical and infrared. The model can also explain the observed galaxy number counts at 850 m, but only if we assume a top-heavy initial mass function for the stars formed in bursts. The predicted redshift distribution of SMGs depends relatively little on their flux over the range 1-10 mJy, with a median value of z 2.0 at a flux of 5 mJy, in good agreement with the recent measurement by Chapman et al. The counts of SMGs are predicted to be dominated by ongoing starbursts. However, in the model these bursts are responsible for making only a few per cent of the stellar mass locked up in massive ellipticals at the present day.