Inferring the redshift distribution of the cosmic infrared background

Cross-correlating the Planck High Frequency Instrument (HFI) maps against quasars from the Sloan Digital Sky Survey (SDSS) DR7, we estimate the intensity distribution of the Cosmic Infrared Background (CIB) over the redshift range 0 < z < 5.We detect redshift-dependent spatial cross-correlations between the two datasets using the 857, 545 and 353 GHz channels and we obtain upper limits at 217 GHz consistent with expectations. At all frequencies with detectable signal we infer a redshift distribution peaking around z ~ 1.2 and find the recovered spectrum to be consistent with emission arising from star forming galaxies. By assuming simple modified blackbody and Kennicutt relations, we estimate dust and star formation rate density as a function of redshift, finding results consistent with earlier multiwavelength measurements over a large portion of cosmic history. However, we note that, lacking mid-infrared coverage, we are not able to make an accurate determination of the mean temperature for the dust responsible for the CIB. Our results demonstrate that clustering-based redshift inference is a valuable tool for measuring the entire evolution history of the cosmic star formation rate from a single and homogeneous dataset.