Euclid: Exploring observational systematics in cluster cosmology -- a comprehensive analysis of cluster counts and clustering

TL;DR

This work develops a comprehensive framework to extract cosmology from Euclid-like clusters by explicitly modelling observational and modelling systematics in cluster counts and clustering, and by validating joint analyses with 1000 PINOCCHIO-based mocks. It couples number counts, the 3D cluster 2PCF, and weak-lensing mean mass within a unified likelihood, incorporating photo-z uncertainties, redshift-space distortions, IR resummation, and detailed covariance modelling. The key finding is that combining all three probes yields FoM improvements by more than a factor of three over counts alone, with the two probes effectively uncorrelated and covariance dependence largely mitigated in the joint fit; photo-z errors broaden posteriors by ~20–30%, while RSDs can bias results if neglected. Information is driven by BAO-scale clustering near 60–130 h⁻1 Mpc, while larger scales contribute little;accurate covariance modelling is essential, especially for counts which are sensitive to redshift distortions in the sample variance term. Overall, the results provide a robust blueprint for exploiting Euclid’s cluster data, guiding where to focus modelling efforts and highlighting the substantial gains from a full-probe analysis.

Abstract

This study explores the impact of observational and modelling systematic effects on cluster number counts and cluster clustering and provides model prescriptions for their joint analysis, in the context of the \Euclid survey. Using 1000 \Euclid-like cluster catalogues, we investigate the effect of systematic uncertainties on cluster summary statistics and their auto- and cross-covariance, and perform a likelihood analysis to evaluate their impact on cosmological constraints, with a focus on the matter density parameter $Ω_{\rm m}$ and on the power spectrum amplitude $σ_8$. Combining cluster clustering with number counts significantly improves cosmological constraints, with the figure of merit increasing by over 300\% compared to number counts alone. We confirm that the two probes are uncorrelated, and the cosmological constraints derived from their combination are almost insensitive to the cosmology dependence of the covariance. We find that photometric redshift uncertainties broaden cosmological posteriors by 20--30\%, while secondary effects like redshift-space distortions (RSDs) have a smaller impact on the posteriors -- 5\% for clustering alone, 10\% when combining probes -- but can significantly bias the constraints if neglected. We show that clustering data below $60\,h^{-1}\,$Mpc provides additional constraining power, while scales larger than acoustic oscillation scale add almost no information on $Ω_{\rm m}$ and $σ_8$ parameters. RSDs and photo-$z$ uncertainties also influence the number count covariance, with a significant impact, of about 15--20\%, on the parameter constraints.

Figures (14)

• Figure 1: Cross-covariance between number counts and clustering. For better visualisation, here we use redshift bins of width $\Delta z=0.2$ for counts and $\Delta z=0.5$ for the 2PCF. Left: Auto- and cross-correlation matrix of number counts and clustering, computed from 1000 mocks. Right: Log-likelihood residuals for number counts and clustering, for each one of the 1000 lightcones, with respect to the mean value assuming the fiducial model parameters.
• Figure 2: Parameter posterior distributions with 68% and 95% confidence intervals, from different combinations of probes: number counts and weak lensing mass in blue, clustering and weak lensing mass in orange, number counts and clustering in green, and all the three probes in red. Dotted grey lines are the input cosmology of the catalogues.
• Figure 3: Marginalised posterior distributions in the $\Omega_{\rm m}$--$\sigma_8$ plane, with 68% and 95% confidence intervals, using fixed-cosmology (filled contours), cosmology-dependent (empty contours), or wrong ($\Omega_{\rm m}=0.320$, $\sigma_8=0.775$, dashed empty contours) covariance matrix. Lower left panel is for clustering and weak lensing masses alone, while upper right panel is for full-probe combination.
• Figure 4: Impact of photo-$z$ uncertainties on the 2PCF. Left panel: 2PCF prediction for different values of photo-$z$ uncertainty, $\sigma_{z0}=0$ in red, $\sigma_{z0}=0.005$ in orange, and $\sigma_{z0}=0.01$ in blue. This is for the redshift bin $z = 0.4$--$0.8$. Right panel: Marginalised posterior distributions in the $\Omega_{\rm m}$--$\sigma_8$ plane, with 68% and 95% confidence intervals, from the combination of clustering and weak lensing masses for the three cases in the left panel.
• Figure 5: Systematic effects introduced by neglecting redshift distortions in 2PCF modelling. Left: 2PCF residuals with respect to the full model (that is, photo-$z$, RSDs, IR resummation, and GD correction) for the three cases: model without RSDs (blue line); model without IR resummation (red line); model without GD correction (green line). Shaded areas are given by the square root of the diagonal covariance divided by the number of mocks. Right: Marginalised posterior distributions in the $\Omega_{\rm m}$--$\sigma_8$ plane, with 68% and 95% confidence intervals, from the combination of clustering and weak lensing masses for the three cases represented in the left panel (same colour code), compared to the full redshift effects case (black empty contours). Dotted grey lines are the input cosmology of the catalogues.