Optimizing future experiments of cosmic far-infrared background: a principal component approach

The anisotropies of cosmic far-infrared background (CFIRB) probe the star formation rate (SFR) of dusty star-forming galaxies as a function of dark matter halo mass and redshift. We explore how future CFIRB experiments can optimally improve the SFR constraints beyond the current measurements of Planck. We introduce a modelindependent, piecewise parametrization for SFR as a function of halo mass and redshift, and we calculate the Fisher matrix and principal components of these parameters to estimate the SFR constraints of future experiments. We investigate how the SFR constraints depend on angular resolution, number and range of frequency bands, survey coverage, and instrumental sensitivity. We find that the angular resolution and the instrumental sensitivity play the key roles. Improving the angular resolution from 20 to 4 arcmin can improve the SFR constraints by 1.5–2.5 orders of magnitude. With the angular resolution of Planck, improving the sensitivity by 10 or 100 times can improve the SFR constraints by one or two orders of magnitude, and doubling the number of frequency bands can also improve the SFR constraints by an order of magnitude. We find that survey designs like the Cosmic Origins Explorer (CORE) are very close to the optimal design for improving the SFR constraints at all redshifts, while survey designs like LiteBIRD and CMB-S4 can significantly improve the SFR constraints at z & 3.