KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey

This paper asks how well the completed Kilo-Degree Survey (KiDS) can constrain late-time structure growth and cosmology using cosmic shear, and—crucially—whether the resulting constraints remain consistent with the high-redshift expectations from the Planck CMB. This matters because weak-lensing measurements of the clustering amplitude have, for about a decade, tended to yield lower values of the commonly used amplitude combination $S_8\equiv {\sigma }_8\sqrt{{\Omega }_m/0.3}$ than Planck, contributing to the so-called $S_8$ tension. Resolving whether this is a statistical fluctuation, a modeling/systematic issue (e.g., photometric redshift calibration, intrinsic alignments, baryonic feedback, or shear calibration), or a genuine cosmological discrepancy is central to the field’s transition from “stage-III” to “stage-IV” lensing surveys.

The authors present the KiDS-Legacy cosmic shear analysis using the final KiDS data release (KiDS-dr5). The completed KiDS footprint covers 1347 deg${}^2$ of deep nine-band imaging (optical plus NIR) and includes an additional 23 deg${}^2$ of KiDS-like calibration observations from deep spectroscopic surveys. The analysis extends the lensed galaxy sample to photometric redshift $z_B\le 2.0$ by improving the redshift distribution estimation methodology and by using enhanced calibration data and multi-band image simulations.

Methodologically, the study follows a standard catalogs-to-cosmology pipeline implemented in the CosmoPipe framework. The core observable is the cosmic shear two-point signal, but the paper emphasizes that different summary statistics weight angular scales differently and can therefore respond differently to systematics. The authors measure two-point correlation functions ${\xi }_{\pm }(\theta )$ but do not use them as the primary cosmological data vector due to concerns about scale-mixing and E/B-mode leakage in the presence of masks. Instead, the fiducial cosmological inference uses COSEBIs $E_n$ and band powers $C_{\mathrm{E}}$, both constructed from linear combinations of finely binned ${\xi }_{\pm }$ over $\theta \in [2,300]$ arcmin. They use six tomographic bins (with effective number density $n_{\mathrm{eff}}=8.79$ arcmin${}^{-2}$ after calibration and masking) and include multiplicative shear calibration uncertainty via marginalization. The analysis uses analytic covariance modeling with the OneCovariance code, including Gaussian sample-variance and shot-noise terms, non-Gaussian contributions, and super-sample covariance; covariance predictions are validated against GLASS mocks.

For theoretical modeling, the paper computes shear power spectra using Limber-approximated projections of the non-linear matter power spectrum. The non-linear matter power spectrum is modeled with HMCode2020 (calibrated against simulations) rather than Halofit, and the analysis marginalizes over uncertainty in baryonic feedback through the HMCode2020 AGN feedback parameter ${\log }_{10}(T_{\mathrm{AGN}}/K)$. Intrinsic alignments (IA) are treated with a new physically motivated model: the fiducial IA model (NLA-$M$) makes the alignment amplitude depend on both the fraction of early-type (“red”) galaxies and their host halo mass distribution. The paper also tests alternative IA models (NLA baseline, NLA-$z$ with redshift evolution, and a restricted TATT scale-dependent extension NLA-$k$).

Key results are reported primarily in terms of ${\Sigma }_8\equiv {\sigma }_8({\Omega }_m/0.3{)}^{\alpha }$, where $\alpha$ is optimized to match the degeneracy direction of the KiDS dataset. The fiducial COSEBIs-based constraint is $${\Sigma }_8=0.821_{-0.016}^{+0.014}$$ (with $\alpha =0.58$). In the more traditional $S_8$ parametrization, the fiducial COSEBIs result is $$S_8=0.815_{-0.021}^{+0.016}$$ (also reported as $S_8=0.815_{-0.021}^{+0.016}$ for the marginal mode and HPDI summary). The paper states that this is in agreement with Planck Legacy at the $0.73\sigma$ level in ${\Sigma }_8$ (and discusses Hellinger-distance-based consistency metrics). Compared to previous KiDS analyses, the authors claim an improvement in constraining power of about $\sim 32\%$ in ${\Sigma }_8$, driven by increased survey area, deeper redshift reach, improved redshift distribution estimation, and enhanced calibration/image reduction.

The paper also quantifies robustness to modeling choices. Replacing the emulator-based non-linear power spectrum predictions with direct camb calculations changes the recovered ${\Sigma }_8$ by at most $0.03\sigma$. Switching off non-Gaussian covariance terms reduces the uncertainty by $12\%$ to $19\%$ but does not significantly shift the central value ($\Delta {\Sigma }_8\approx 0.02\sigma$), indicating that non-Gaussian scales contribute meaningfully to the constraining power. Varying intrinsic alignment models produces mild shifts in $S_8$ and ${\Sigma }_8$ (maximal differences up to $0.17\sigma$ for $C_{\mathrm{E}}$, and up to $0.54\sigma$ for $E_n$ in some comparisons), while changing IA model choice can reduce constraining power by $\sim 12\%$ to $13\%$ for NLA-$z$ relative to NLA-$M$. Redshift calibration variations generally keep ${\Sigma }_8$ consistent (typically $\Delta {\Sigma }_8\le 0.17\sigma$), while using MICE2-calibrated $N(z)$ (less realistic at high redshift) can shift ${\Sigma }_8$ upward by as much as $1.25\sigma$, which the authors treat as inferior to the fiducial SKiLLS-based calibration.

A notable systematic-control component is the null testing program. The authors perform PSF modeling residual tests, PSF leakage tests, and B-mode tests. They report that PSF modeling and PSF leakage contamination are negligible relative to statistical uncertainties (typically below a $10\%$ benchmark). For B modes, an astrometric issue was identified during the blinded phase, leading to additional masking of $\sim 4\%$ of sources (46.6 deg${}^2$ removed from the initial footprint). After this, the B-mode p-values across all tomographic combinations pass their threshold $p>0.01$ for the fiducial COSEBIs-based analysis.

Finally, the paper uses the agreement with Planck to infer constraints on baryonic feedback amplitude. With cosmological parameters fixed to Planck values, they place an upper limit on baryon feedback of ${\log }_{10}(T_{\mathrm{AGN}}/K)\le 7.71$ at 68% confidence and $\le 8.01$ at 95% confidence. In the fiducial analysis, the MAP estimate lies at the lower prior boundary, and the marginal posterior is skewed toward negligible feedback, implying little evidence for strong baryonic suppression in the scales to which KiDS is most sensitive.

Limitations are mostly implicit in the modeling and validation choices: the analysis relies on Limber approximation (argued to be adequate because IA contributes only $\sim 10\%$ of the signal and because the analysis uses $\ell \gtrsim 50$); it uses a specific non-linear power spectrum model (HMCode2020) and a particular baryonic feedback parametrization; and it uses physically motivated IA modeling with priors informed by external direct alignment measurements. The authors also acknowledge that ${\xi }_{\pm }$ are less reliable due to scale-mixing and non-Gaussian likelihood behavior on large scales, and therefore do not use them as the primary inference vector. Additionally, while covariance modeling is validated against mocks to within $\sim 5\%$ to $10\%$ depending on scale, analytic covariance remains an approximation.

Practically, the results provide a high-robustness stage-III weak-lensing benchmark: the KiDS-Legacy dataset is reported as the most internally robust KiDS sample to date (with a companion paper providing extensive internal/external consistency tests). For cosmologists and survey teams, the main takeaway is that improved redshift calibration and survey characterization can bring cosmic shear constraints into strong consistency with Planck in $S_8$/${\Sigma }_8$, reducing the impetus to invoke new physics at this stage. For future stage-IV analyses (Euclid, Rubin/LSST, Roman), this work also supplies a template for how to manage redshift systematics, IA modeling, baryonic feedback marginalization, and end-to-end null testing—especially the importance of astrometric systematics and the use of physically motivated IA models.

Overall, the paper’s core contribution is a precise, carefully validated cosmic shear constraint from the complete KiDS survey, yielding ${\Sigma }_8\approx 0.821$ with $\sim 0.016$ uncertainty and demonstrating $\lesssim 1\sigma$ agreement with Planck, while showing that the remaining modeling/systematic uncertainties are controlled at the level required for stage-III cosmology and for informing stage-IV expectations.