  Star-forming galaxies which are too faint to be detected individually produce
intensity fluctuations in the cosmic background light. This contribution needs
to be taken into account as a foreground when using the primordial signal to
constrain cosmological parameters. The extragalactic fluctuations are also
interesting in their own right as they depend on the star formation history of
the Universe and the way in which this connects with the formation of cosmic
structure. We present a new framework which allows us to predict the occupation
of dark matter haloes by star-forming galaxies and uses this information, in
conjunction with an N-body simulation of structure formation, to predict the
power spectrum of intensity fluctuations in the infrared background. We compute
the emission from galaxies at far-infrared, millimetre and radio wavelengths.
Our method gives accurate predictions for the clustering of galaxies both for
the one halo and two halo terms. We illustrate our new framework using a
previously published model which reproduces the number counts and redshift
distribution of galaxies selected by their emission at $850\,\mu$m. Without
adjusting any of the model parameters, the predictions show encouraging
agreement at high frequencies and on small angular scales with recent estimates
of the extragalactic fluctuations in the background made from early data
analysed by the Planck Collaboration. There are, however, substantial
discrepancies between the model predictions and observations on large angular
scales and at low frequencies, which illustrates the usefulness of the
intensity fluctuations as a constraint on galaxy formation models.
