Euclid preparation. Impact of redshift distribution uncertainties on the joint analysis of photometric galaxy clustering and weak gravitational lensing

Published 1 Apr 2026 in astro-ph.CO | (2604.00805v1)

Abstract: One of the $\textit{Euclid}$ mission's key projects is the so-called 3$\times$2pt analysis, that is, the combination of cosmic shear, photometric galaxy clustering, and galaxy-galaxy lensing. Although $\textit{Euclid}$ has established quality requirements for the photo-$z$ accuracy needed for the weak lensing galaxy sample, no such requirements have been set for the photometric clustering sample. In this paper, we investigate the impact of redshift uncertainties on $\textit{Euclid}$'s photometric galaxy clustering analysis and its combination with weak gravitational lensing, focusing on data release 1 (DR1). In particular, we study whether having precise knowledge of the mean of the redshift distributions per bin is sufficient to avoid biases in the resulting cosmological constraints or whether accuracy in the higher-order moments of the distribution is required. We evaluate the results based on their constraining power on $w_{\mathrm{0}}$ and $w_{a}$ and define thresholds for the precision and accuracy of $\textit{Euclid}$'s redshift distribution of the photometric clustering sample. We find that the redshift distributions of the photometric clustering sample must be known at an accuracy of 0.004(1+$z$) in the mean in order to recover 80$\%$ of the constraining power in $\textit{Euclid}$'s DR1 $w_{\mathrm{0}}w_{a}$CDM 3$\times$2pt analysis. The impact of the uncertainty on the width is negligible, provided the mean redshift is constrained with sufficient accuracy. For most sources of redshift distribution error, attaining the requirement on the mean will also reduce uncertainty in the width well below the required level.

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Summary

The paper quantifies the degradation in dark energy constraints, showing that lens redshift means must be calibrated to ≤0.004(1+z) to recover 80% of performance.
It employs Monte Carlo and Fisher forecasts to assess systematic biases from shifts in the redshift mean and variations in the distribution width.
The study defines clear thresholds for Euclid DR1, streamlining redshift calibration in multi-probe analyses and guiding future survey designs.

Impact of Redshift Distribution Uncertainties on Joint Photometric Galaxy Clustering and Weak Lensing Cosmological Analysis in Euclid DR1

Introduction

The Euclid mission aims to enable high-precision cosmological inference through the combination of photometric galaxy clustering, cosmic shear, and galaxy-galaxy lensing—the so-called 3×2pt analysis. The accuracy of tomographic redshift distributions, particularly for the galaxy samples used as lenses in clustering measurements, is a critical source of systematic uncertainty, yet the requirements for the photo-z accuracy of lens galaxies have not been previously specified with the same rigor as for the source (shear) sample. This work provides a comprehensive investigation of how uncertainties in the mean and width of lens redshift distributions propagate to cosmological parameters, quantifies the resulting loss of constraining power, and establishes requirements for redshift calibration in Euclid Data Release 1 (DR1).

Simulation Inputs and Theoretical Framework

A robust theoretical modelling framework is adopted for the analysis: galaxy clustering is computed using the angular correlation function $w(\theta)$ with bias and redshift-space distortions, galaxy-galaxy lensing is modelled via cross-correlations of lens galaxy positions and source galaxy shears, and cosmic shear is captured via tomographic two-point functions. All calculations include advanced treatments such as point-mass marginalization for galaxy-galaxy lensing and the mitigation of baryonic and nonlinear bias through scale cuts. Systematic effects considered include multiplicative and additive shear bias, magnification bias, and intrinsic alignments (modelled with a non-linear alignment model and redshift-dependent amplitude).

Redshift distributions for both sources and lenses are derived from the Euclid Flagship simulation, using six equipopulated tomographic bins per sample, with realistic magnitude limits. The redshift range for both is $0.2

Figure 1: Normalized redshift distributions for source (top) and lens (bottom) galaxies from the Flagship simulation for a DR1-like configuration.

Monte Carlo and Fisher-matrix based approaches are employed for cosmological forecasts, utilizing CosmoSIS and CosmoCov. The parameter space includes standard $\Lambda$ CDM and $w_0w_a$ CDM cosmological parameters, galaxy bias, and nuisance parameters for IA, photo-z errors, and shear calibration.

Marginalization over Redshift Distribution Uncertainties: Loss of Constraining Power

A primary result concerns how marginalization over uncertainties in the mean ( $\Delta z$ ) and width ( $\sigma_z$ ) of the lens $n(z)$ degrades the constraining power on dark energy parameters. The loss is quantified using the Figure of Merit (FoM) for $w_0$ – $w_a$ and $\Omega_{\textrm{m}}$ –$0.2

Figure 2: Cosmological posteriors for $0.2

Fisher forecasts corroborate these results and allow rapid exploration of parameter dependence. The constraining power falls off steeply when the mean redshift uncertainty exceeds $0.2 $\Lambda$

Biases from Incorrect Redshift Distribution Modeling

Complementary runs perturb the adopted lens $\Lambda$ 2 by shifting the mean or stretching the width, without marginalizing over the associated nuisance parameters, to assess induced biases in cosmological parameter estimates. Key findings include:

For the full 3×2pt $\Lambda$ 3CDM analysis, even a shift in the mean of 0.002(1+ $\Lambda$ 4) in the lens $\Lambda$ 5 produces a bias $\Lambda$ 6 in $\Lambda$ 7 and $\Lambda$ 8, violating standard thresholds for acceptable systematic error budgets.
Bias from $\Lambda$ 9 width is subdominant in joint analyses unless it is perturbed by an order of magnitude larger than allowed for the mean.
For photometric clustering alone, both mean and width are comparably important; a 0.2% stretch in width impacts $w_0w_a$ 0 nearly as much as a 0.2% shift in the mean.

Figure 3: Impact of shifts (left) and stretches (right) in the lens $w_0w_a$ 1 on $w_0w_a$ 2– $w_0w_a$ 3 confidence contours; shifts dominate biases, width is only important when highly excessive.

Figure 4: Biases on $w_0w_a$ 4, $w_0w_a$ 5, and $w_0w_a$ 6 for photometric clustering only; width and mean both significantly affect clustering-only analyses.

Implications for Survey Design and Future Developments

Dominance of Mean Requirement: For joint 3×2pt (clustering + shear + galaxy-galaxy lensing) analyses, the critical requirement is the calibration of the mean of each lens $w_0w_a$ 7 to within $w_0w_a$ 8. The width is constrained implicitly by the mean in typical calibration scenarios.
Width More Critical for Clustering-Only: Galaxy clustering and its observables, being less integrated over redshift, are more sensitive to the detailed width of $w_0w_a$ 9. Therefore, analyses that do not combine with shear/g-g lensing require more stringent control over both moments.
Marginalization Suffices: Marginalizing over the mean with appropriate priors suffices to guard against bias and excessive degradation, providing a practical approach for cosmological inference in the presence of realistic redshift uncertainties.
DR3 Outlook: With larger DR3 datasets and improved spectroscopic coverage, the data will self-calibrate nuisance parameters more effectively, allowing weaker priors (up to $\Delta z$ 0) before significant degradation of cosmological constraints occurs (see also [Blot25], [canas2025euclid]).

Conclusion

This analysis provides the first quantitative requirement on lens photo-z calibration for Euclid DR1: the mean of each lens galaxy tomographic bin must be known to $\Delta z$ 1 accuracy. This ensures biases on cosmological parameters remain below $\Delta z$ 2 and preserves at least 80% of the $\Delta z$ 3– $\Delta z$ 4 figure of merit in the critical 3×2pt analysis. The result that width becomes negligible when the mean is accurately calibrated simplifies operational requirements and highlights the value of joint probe analyses. For Euclid DR1, the galaxy clustering redshift calibration is not the limiting factor on cosmological power, so long as the more stringent source sample requirements are met. Future surveys with even greater calibration samples will benefit further, with the dominant challenge remaining the control of source sample photo-z systematics.

Overall, the work defines clear, achievable thresholds for DR1, directly informs analysis pipelines for upcoming Euclid cosmological analyses, and offers a unified framework for propagating redshift calibration uncertainties in multi-probe large-scale structure inference.

References

Euclid Collaboration: Bertmann et al., "Euclid preparation. Impact of redshift distribution uncertainties on the joint analysis of photometric galaxy clustering and weak gravitational lensing" (2604.00805).
Euclid Collaboration: Castander et al., "Euclid - V. The Flagship galaxy mock catalogue: A comprehensive simulation for the Euclid" [EuclidSkyFlagship].
Dark Energy Survey Collaboration: Porredon et al., "Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and galaxy-galaxy lensing..." [Porredon2022].
Blot et al., "Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 6: Impact of systematic uncertainties on the cosmological analysis" [Blot25].
Ca~nas-Herrera et al., "Euclid preparation: Cosmology Likelihood for Observables in Euclid (CLOE). 3. Inference and Forecasts" [canas2025euclid].