This paper forecasts how the Euclid satellite, together with maps of the cosmic infrared background (CIB) from Planck, can be used to measure when and where stars formed across much of cosmic history. The CIB is light from dust heated by young stars. By comparing that diffuse infrared glow to maps of galaxy positions and weak gravitational lensing from Euclid, the authors show it is possible to separate contributions from different redshifts and recover a bias‑weighted measure of the star‑formation rate density over time.

The authors use simulated Euclid data for photometric galaxy clustering (how galaxies cluster on the sky) and tomographic weak lensing (lens signals split into redshift slices), and cross‑correlate those with Planck CIB maps. They build templates from a halo occupation distribution (HOD) model—a way to connect galaxies and star formation to the dark matter haloes that host them—and fit for the quantity ⟨b ρ_SFRD⟩. This quantity is the star‑formation‑rate density multiplied by a “bias” factor that describes how strongly the star‑forming sources trace the underlying matter. The forecasts are quantified with Fisher information matrix calculations.

At a conceptual level the method works because the CIB is a projected signal that mixes emission from many redshifts, while Euclid’s tomographic galaxy and shear samples give redshift information. Cross‑correlating them ties CIB emission to the large‑scale structure at specific redshifts, letting the team recover the redshift evolution of the bias‑weighted star formation. To keep the analysis robust they focus on large scales (wave numbers k < 0.3 h Mpc⁻¹ and angular multipoles ℓ ≥ 100), where a two‑halo clustering term dominates. They also include shot noise in the error estimates and apply a Bernardeau–Nishimichi–Taruya (BNT) nulling step for the shear data to reduce certain lensing systematics.