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 model-independent, 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.
