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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.
Their forecasts indicate that adding Euclid will tighten constraints on ⟨b ρ_SFRD⟩ by about a factor of two across all redshift bins compared with previous work using similar data. The method also yields improved constraints on HOD parameters: marginalized uncertainties typically shrink by roughly a factor of 2.5, and previously degenerate parameters become better separated. The paper reports these gains come while extending measurements to a deeper redshift range than earlier analyses.
This approach matters because the CIB is a sensitive tracer of star formation, especially around “cosmic noon” (redshift z ≈ 1–2), when the Universe formed stars most actively. Cross‑correlations with Euclid provide a way to use the full-sky CIB maps to learn about star formation at different times, without relying on catalogues of individually detected far‑infrared galaxies—which are hard to build at high redshift.
Important caveats remain. These results are forecasts based on simulations and on templates from an HOD model rather than direct data. The analysis deliberately avoids small angular scales where one‑halo (within‑halo) effects and nonlinear physics become important; extending to those scales would require more complex modeling. The recovery is of a bias‑weighted star‑formation quantity (⟨b ρ_SFRD⟩), not the plain star‑formation rate density, so interpreting the result in terms of absolute star‑formation history depends on the modeling of that bias. The work also assumes a specific fiducial cosmology and uses Planck CIB maps, which have limited angular resolution; real data may introduce additional systematics. The authors test some choices (for example, their ℓmin cut) and find little sensitivity within reasonable ranges, but the final accuracy will depend on how well the templates and systematics are controlled in practice.