A simple and versatile parameterized approach to the star formation history allows a quantitative investigation of the constraints from far infrared and submillimetre counts and background intensity measurements .

The models include four spectral components : infrared cirrus ( emission from interstellar dust ) , an M82-like starburst , an Arp220-like starburst and an AGN dust torus .
The 60 \mu m luminosity function is determined for each chosen rate of evolution using the PSCz redshift data for 15000 galaxies .
The proportions of each spectral type as a function of 60 \mu m luminosity are chosen for consistency with IRAS and SCUBA colour-luminosity relations , and with the fraction of AGN as a function of luminosity found in 12 \mu m samples .
The luminosity function for each component at any wavelength can then be calculated from the assumed spectral energy distributions .
With assumptions about the optical seds corresponding to each component and , for the AGN component , an assumed dependence of the dust covering factor on luminosity , the optical and near infrared counts can be accurately modelled .
High and low mass stars are treated separately , since the former will trace the rate of star formation , while the latter trace the cumulative integral of the star formation rate .

A good fit to the observed counts at 0.44 , 2.2 , 15 , 60 , 90 , 175 and 850 \mu m can be found with pure luminosity evolution in all 3 cosmological models investigated : \Omega _ { o } = 1 , \Omega _ { o } = 0.3 ( \Lambda = 0 ) , and \Omega _ { o } = 0.3 , \Lambda = 0.7 .

All 3 models also give an acceptable fit to the integrated background spectrum .
Selected predictions of the models , for example redshift distributions for each component at selected wavelengths and fluxes , are shown .
The efect of including an element of density evolution is also investigated .

The total mass-density of stars generated is consistent with that observed , in all 3 cosmological models .