Star formation history from the cosmic infrared background anisotropies

We present a linear clustering model of cosmic infrared background (CIB) anisotropies at large scales that is used to measure the cosmic star formation rate density up to redshift 6, the effective bias of the CIB, and the mass of dark matter halos hosting dusty starforming galaxies. This is achieved using the Planck CIB auto-and cross-power spectra (between different frequencies) and CIB x CMB (cosmic microwave background) lensing cross-spectra measurements, as well as external constraints (e.g. on the CIB mean brightness). We recovered an obscured star formation history which agrees well with the values derived from infrared deep surveys and we confirm that the obscured star formation dominates the unobscured formation up to at least z = 4. The obscured and unobscured star formation rate densities are compatible at 1 sigma at z = 5. We also determined the evolution of the effective bias of the galaxies emitting the CIB and found a rapid increase from similar to 0.8 at z = 0 to similar to 8 at z = 4. At 2 < z < 4, this effective bias is similar to that of galaxies at the knee of the mass functions and submillimetre galaxies. This effective bias is the weighted average of the true bias with the corresponding emissivity of the galaxies. The halo mass corresponding to this bias is thus not exactly the mass contributing the most to the star formation density. Correcting for this, we obtained a value of log(M-h/M-circle dot) = 12.77(-0.125)(+0.28) for the mass of the typical dark matter halo contributing to the CIB at z = 2. Finally, using a Fisher matrix analysis we also computed how the uncertainties on the cosmological parameters affect the recovered CIB model parameters, and find that the effect is negligible.