The mid-infrared local luminosity function is evolved with redshift to fit the spectrum of the cosmic infrared background ( CIRB ) at \lambda > 5 \mu m and the galaxy counts from various surveys at mid-infrared , far-infrared and submillimeter wavelengths .
A variety of evolutionary models provide satisfactory fits to the CIRB and the number counts .
The degeneracy in the range of models can not be broken by current observations .
However , the different evolutionary models yield approximately the same comoving number density of infrared luminous galaxies as a function of redshift .
Since the spectrum of the cosmic background at \lambda > 200 \mu m is quite sensitive to the evolution at high redshift , i.e . z > 1 , all models that fit the counts require a flattening at z \sim 0.8 to avoid overproducing the CIRB .
About 80 % of the 140 \mu m CIRB is produced at 0 < z < 1.5 while only about 30 % of the 850 \mu m background is produced within the same redshift range .
The nature of the evolution is then translated into a measure of the dust enshrouded star formation rate density as a function of redshift and compared with estimates from rest-frame optical/ultraviolet surveys .
The dust obscured star formation rate density appears to peak at z = 0.8 \pm 0.1 , much sooner than previously thought , with a value of 0.25 ^ { +0.12 } _ { -0.1 } M _ { \sun } yr ^ { -1 } Mpc ^ { -3 } , in excellent agreement with a value derived from extinction correction to NICMOS observations , and remains almost constant up to z \sim 2 .
At least 70 % of this star formation takes place in infrared luminous galaxies with L _ { IR } > 10 ^ { 11 } ~ { } L _ { \sun } .
The long wavelength observations that constrain our evolutionary models do not strongly trace the evolution at z > 2 and a drop off in the dust enshrouded star formation rate density is consistent with both the CIRB spectrum and the number counts .
However , a comparison with the infrared luminosity function derived from extinction corrected rest-frame optical/ultraviolet observations of the Lyman-break galaxy ( LBG ) population at z \sim 3 suggests that the almost flat comoving star formation rate density seen between redshifts 0.8 and 2 , extends up to a redshift of z \sim 4 .