2025ApJ...992...65C

The cosmic far-infrared background (CIB) encodes dust emission from all galaxies and carries valuable information on structure formation, star formation, and chemical enrichment across cosmic time. However, its redshift-dependent spectrum remains poorly constrained due to line-of-sight projection effects. We address this by cross-correlating 11 far-infrared intensity maps spanning a 50-fold frequency range from Planck, Herschel, and Infrared Astronomical Satellite, with spectroscopic galaxies and quasars from Sloan Digital Sky Survey I-IV tomographically. We mitigate foregrounds using a CIB-free Milky Way dust map. These cross-correlation amplitudes on two-halo scales trace bias-weighted CIB redshift distributions and collectively yield a 60σ detection of the evolving CIB spectrum, sampled across hundreds of rest-frame frequencies over 0 < z < 4. We break the bias-intensity degeneracy by adding monopole information from FIRAS+Planck. The recovered spectrum reveals a dust temperature distribution that is broad, spanning the full range of host environments, and moderately evolving. Using low-frequency CIB amplitudes, we constrain cosmic dust density, Ω_dust, which peaks at z = 1-1.5 and declines threefold to the present. Our broad spectral coverage enables a determination of the total infrared luminosity density to 0.04 dex statistical precision, tracing star formation history with negligible cosmic variance across 90% of cosmic time. We find that cosmic star formation is 80% dust-obscured at z = 0 and 60% at z = 4. Our results, based on intensity mapping, are complete, requiring no extrapolation to faint galaxies or low-surface-brightness components. We release our tomographic CIB spectrum and redshift distributions as a public resource for future studies of the CIB, both as a cosmological matter tracer and cosmic microwave background foreground.