KiDS-1000: Cosmological Data Release

• KiDS-1000 is the fourth data release of the Kilo-Degree Survey, covering 1006 deg² in nine optical-to-near-IR bands and providing calibrated weak-lensing measurements.
• The survey employs deep r-band imaging with precise PSF modelling and tomographic binning to achieve robust redshift calibration and shape estimation for 21 million galaxies.
• Advanced analyses using KiDS-1000 data constrain the structure-growth parameter S8 and address systematics via techniques like MetaCalibration and simulation-based inference.

Searching arXiv for recent KiDS-1000 papers to ground the article. KiDS-1000 is the fourth data release of the Kilo-Degree Survey, covering 1006 deg$^2$ in nine optical-to-near-infrared bands, $ugriZYJHK_s$, from VST/OmegaCAM and VIKING/VISTA, and optimized for weak lensing. For weak-lensing analyses, the release is typically described through an effective unmasked area of $777.4$ deg$^2$, a “gold sample” of 21 million galaxies with calibrated redshift distributions, and five tomographic source bins spanning $0.1<z_B\le1.2$ (Giblin et al., 2020, Hildebrandt et al., 2020). KiDS-1000 has been used for cosmic shear, galaxy-galaxy lensing, spectroscopic clustering, higher-order shear statistics, density split statistics, peak counts, cluster abundance and weak lensing, CMB-lensing cross-correlation, and simulation-based inference, with repeated emphasis on the structure-growth parameter $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$ and on the control of shear, redshift, intrinsic-alignment, and baryonic systematics (Heymans et al., 2020, Burger et al., 2023, Wietersheim-Kramsta et al., 2024).

1. Survey definition and catalogue construction

KiDS-1000 combines deep $r$-band imaging for shape measurement with matched nine-band photometry for photometric redshifts. The $r$-band weak-lensing data were observed under the requirement that the PSF full-width at half maximum is $<0.8''$, yielding a mean seeing of $0.7''$ and a median $ugriZYJHK_s$0 point-source depth of $ugriZYJHK_s$1 mag in a $ugriZYJHK_s$2 aperture (Giblin et al., 2020). Shape estimation is based on the model-fitting algorithm lensfit, applied to the set of unstacked $ugriZYJHK_s$3-band exposures, with each galaxy assigned an ellipticity $ugriZYJHK_s$4 and a weight $ugriZYJHK_s$5 (Giblin et al., 2020).

The release is often summarized through a small set of survey-level quantities.

Quantity	Value	Source
Total imaging footprint	$ugriZYJHK_s$6 deg$ugriZYJHK_s$7	(Giblin et al., 2020)
Effective unmasked weak-lensing area	$ugriZYJHK_s$8 deg$ugriZYJHK_s$9	(Giblin et al., 2020)
Gold-sample size	21 million galaxies	(Giblin et al., 2020)
Gold-sample $777.4$0	$777.4$1 arcmin$777.4$2	(Giblin et al., 2020)
Pre-redshift-selection $777.4$3	$777.4$4 arcmin$777.4$5	(Giblin et al., 2020)
Tomographic binning	five bins, $777.4$6	(Hildebrandt et al., 2020)

PSF modelling was constructed on a $777.4$7 pixel grid per exposure, with each pixel represented by a 2D polynomial of order $777.4$8 across the focal plane and of order $777.4$9 per CCD chip, so as to capture discontinuities at chip boundaries (Giblin et al., 2020). The shear catalogue paper states that the PSF model meets the requirement to induce less than a $^2$0 change in the inferred cosmic-shear constraints on $^2$1, and the catalogue-level validation found no evidence for significant non-lensing B-mode distortions in the data (Giblin et al., 2020).

Later reanalyses refined the basic catalogue products rather than replacing the survey definition. The “v2” cosmic-shear analysis updated lensfit from v309c to v321, applied an empirical PSF-leakage correction, and reported that the overall additive bias $^2$2 was halved relative to the v1 catalogue, now at $^2$3 (Li et al., 2023). A still later reanalysis implemented MetaCalibration, obtained $^2$4 arcmin$^2$5 versus $^2$6 arcmin$^2$7 for lensfit in the cosmology sample, and found multiplicative biases $^2$8 in all five cosmology bins (Yoon et al., 1 Oct 2025).

2. Redshift calibration and tomographic binning

KiDS-1000 tomography is defined from BPZ photometric-redshift point estimates $^2$9, with bins $0.1<z_B\le1.2$0 (Hildebrandt et al., 2020). The baseline calibration of the source redshift distributions used deep spectroscopic reference catalogues re-weighted with a self-organising map (SOM) in nine-dimensional magnitude space. If $0.1<z_B\le1.2$1 and $0.1<z_B\le1.2$2 denote the photometric and spectroscopic occupancies of SOM cell $0.1<z_B\le1.2$3, the cell weight is

$0.1<z_B\le1.2$4

and the reweighted redshift distribution is

$0.1<z_B\le1.2$5

A “gold” selection removes cells without spectroscopic support or with a large spectroscopic-photometric discrepancy (Hildebrandt et al., 2020).

Validation on 100 independent KiDS-like MICE realizations found $0.1<z_B\le1.2$6 in all five bins, with $0.1<z_B\le1.2$7 (Hildebrandt et al., 2020). An independent clustering-redshift approach fitted

$0.1<z_B\le1.2$8

and found offsets consistent with zero, with combined uncertainties of order $0.1<z_B\le1.2$9–$S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$0 across the five bins (Hildebrandt et al., 2020). This dual calibration is central to the claim that redshift errors remain a subdominant part of the KiDS-1000 weak-lensing error budget (Hildebrandt et al., 2020).

The redshift calibration was later expanded in a dedicated cosmic-shear reanalysis. That work compiled 17 spectroscopic campaigns across six $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$1 deg$S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$2 “KiDZ” fields, enlarging the spectroscopic sample from $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$3 to $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$4, then to $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$5 with PAUS and to $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$6 with COSMOS2015 photo-$S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$7s (Busch et al., 2022). The fraction of KiDS-1000 source galaxies with reliable calibration rose from $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$8 to $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$9 with the “spec-z fiducial” sample and to $r$0 when PAUS and COSMOS2015 were included, with shifts in $r$1 of at most $r$2 across the tested calibration subsets (Busch et al., 2022).

A more recent development replaced summary redshift calibration with full posterior inference of galaxy properties. The pop-cosmos analysis performed SED fitting for 4 million KiDS-1000 galaxies, validated photometric redshifts against $r$3 DESI DR1 spectroscopic matches, and argued that physically selected source samples can mitigate intrinsic-alignment systematics while preserving statistical power (Halder et al., 3 Feb 2026). This suggests a transition from tomographic samples defined only by $r$4 to source samples defined by posterior physical properties.

3. Shear estimation and summary statistics

The basic KiDS-1000 shear observables are the tomographic two-point correlation functions

$r$5

estimated from weighted galaxy pairs (Giblin et al., 2020). Multiple compressed representations of these two-point functions were developed for KiDS-1000. In the COSEBI basis, the pure-E mode on a finite angular interval is

$r$6

with $r$7 chosen so that only pure E-modes contribute (Burger et al., 2023). KiDS-1000 COSEBI analyses used $r$8, $r$9 in earlier work and $r$0, $r$1 in the improved cosmic-shear analysis (Busch et al., 2022, Li et al., 2023).

A parallel line of work used Fourier-space statistics. The pseudo-$r$2 analysis divided 21,262,011 galaxies into five tomographic bins and measured eight logarithmic bandpowers in the multipole range $r$3 for all auto- and cross-spectra (Loureiro et al., 2021). The method forward-modelled the survey mask through a mixing matrix $r$4, and the B-mode bandpowers were reported to be consistent with zero signal, with no significant residual contamination from E/B-mode leakage (Loureiro et al., 2021). The joint weak-lensing and clustering methodology paper similarly emphasized band powers and related Fourier-space statistics because they are insensitive to the survey mask and display low levels of mode mixing (Joachimi et al., 2020).

KiDS-1000 also supported genuinely non-Gaussian lensing statistics. The third-order aperture-mass statistic is defined from the compensated filter $r$5 and shear-space partner $r$6, with

$r$7

and third moments $r$8 probe the bispectrum of the convergence field (Burger et al., 2023). These higher-order quantities were later combined with COSEBIs in a tomographic cosmology analysis.

4. Modelling, covariance, and inference pipeline

The standard KiDS-1000 cosmology pipeline couples weak-lensing projection kernels, calibrated source redshift distributions, non-linear matter modelling, nuisance-parameter marginalization, and validated covariance models. In the joint weak-lensing and clustering methodology, linear power spectra were computed with CAMB, non-perturbative non-linear matter power with HMCode, and galaxy clustering with a hybrid model that blends one-loop renormalised perturbation theory with halo-model ingredients (Joachimi et al., 2020). In the later cosmic-shear and higher-order analyses, the non-linear matter power spectrum was modelled with HMcode2020, while third-order statistics used BiHalofit for the bispectrum (Li et al., 2023, Burger et al., 2023).

Intrinsic alignments are generally treated with the non-linear alignment model. In the higher-order shear analysis,

$r$9

which induces the familiar $<0.8''$0, $<0.8''$1, and bispectrum analogues (Burger et al., 2023). Baryonic feedback is incorporated either through HMCode nuisance parameters such as $<0.8''$2 or $<0.8''$3, or through multiplicative responses measured from hydrodynamical simulations such as Magneticum (Heymans et al., 2020, Li et al., 2023, Burger et al., 2023). Across these analyses, photo-$<0.8''$4 shifts $<0.8''$5 and shear-calibration uncertainties $<0.8''$6 are propagated as nuisance parameters or additive covariance contributions (Joachimi et al., 2020, Li et al., 2023).

Covariance construction was a major methodological component of KiDS-1000. The joint weak-lensing and clustering methodology used a dedicated suite of more than 20,000 mocks to assess covariance performance and to quantify the impact of survey geometry and spatial variations of survey depth on signals and errors (Joachimi et al., 2020). The same work found that standard point estimates of $<0.8''$7 from a marginal posterior can under-cover the true value and introduced the projected joint highest-posterior-density (PJ-HPD) interval around the multivariate MAP point to improve calibration (Joachimi et al., 2020). This inference convention recurs in later KiDS-1000 analyses.

The simulation-based inference analysis replaced an analytic likelihood by a learned likelihood. KiDS-SBI used 18,000 forward realizations, score compression from 120 data points down to 7 summaries, non-Limber projection via Levin’s method, and log-normal random matter fields on the curved sky (Wietersheim-Kramsta et al., 2024). The forward model included variable depth, PSF anisotropy, shear calibration, and redshift calibration. A key methodological result was that neglecting variable depth and PSF anisotropies can cause $<0.8''$8 to be overestimated by $<0.8''$9, and that fixing the covariance at a fiducial cosmology underestimates uncertainties on $0.7''$0 by $0.7''$1 (Wietersheim-Kramsta et al., 2024).

5. Principal cosmological constraints and the $0.7''$2 issue

Published KiDS-1000 cosmic-shear analyses report closely related but not identical $0.7''$3 constraints. The pseudo-$0.7''$4 analysis found

$0.7''$5

and, when combined with SDSS BAO, RSD, and Ly$0.7''$6, obtained $0.7''$7 (Loureiro et al., 2021). The enhanced redshift-calibration COSEBIs analysis reported

$0.7''$8

while the improved cosmic-shear measurements paper reported

$0.7''$9

where the second uncertainty quantifies systematic shear-calibration uncertainty (Busch et al., 2022, Li et al., 2023). The MetaCalibration reanalysis found

$ugriZYJHK_s$00

with about $ugriZYJHK_s$01 improved constraining power relative to the lensfit analysis, while concluding that the difference with Planck remains at a similar level and is not caused by the shear measurements (Yoon et al., 1 Oct 2025).

The flagship multi-probe KiDS-1000 $ugriZYJHK_s$02pt analysis combined cosmic shear, spectroscopic galaxy clustering from BOSS, and galaxy-galaxy lensing from the KiDS-BOSS and KiDS-2dFLenS overlaps. Its fiducial MAP+PJ-HPD result was

$ugriZYJHK_s$03

with $ugriZYJHK_s$04 lower than Planck by $ugriZYJHK_s$05 (Heymans et al., 2020). In the companion beyond-flat-$ugriZYJHK_s$06CDM study, the same $ugriZYJHK_s$07pt data were found to be fully consistent with $ugriZYJHK_s$08, $ugriZYJHK_s$09 eV at $ugriZYJHK_s$10 CL, and $ugriZYJHK_s$11, with no clear preference for the fiducial flat $ugriZYJHK_s$12CDM model or the tested extensions (Tröster et al., 2020).

A recurrent theme of the KiDS-1000 literature is the “$ugriZYJHK_s$13 tension” with Planck. The quoted significance depends on probe combination, modelling choices, and the tension metric. The improved cosmic-shear measurements paper reported $ugriZYJHK_s$14 (Li et al., 2023), the enhanced redshift-calibration analysis reported $ugriZYJHK_s$15 (Busch et al., 2022), the pseudo-$ugriZYJHK_s$16 analysis reported $ugriZYJHK_s$17 (Loureiro et al., 2021), and the $ugriZYJHK_s$18pt analysis found $ugriZYJHK_s$19 for one-dimensional $ugriZYJHK_s$20 comparisons but $ugriZYJHK_s$21 in the full multidimensional parameter space (Heymans et al., 2020). The beyond-$ugriZYJHK_s$22CDM analysis further showed that one-dimensional $ugriZYJHK_s$23 tension can disappear in $ugriZYJHK_s$24CDM while persisting in the joint $ugriZYJHK_s$25 space (Tröster et al., 2020).

6. Non-Gaussian, multi-probe, and methodological extensions

KiDS-1000 has been a testbed for moving beyond Gaussian two-point statistics. The combined second- and third-order shear analysis performed the first cosmological parameter analysis of KiDS-1000 with COSEBIs and $ugriZYJHK_s$26, using HMcode2020 for the power spectrum, BiHalofit for the bispectrum, an analytic intrinsic-alignment model, and hydrodynamical simulations for baryonic feedback (Burger et al., 2023). A key technical step was the equal-filter-radii ansatz, with $ugriZYJHK_s$27, which reduced the data-vector dimension from $ugriZYJHK_s$28 to 215 while losing only $ugriZYJHK_s$29 of the joint $ugriZYJHK_s$30–$ugriZYJHK_s$31 figure of merit (Burger et al., 2023). The resulting combined constraint was

$ugriZYJHK_s$32

with negligible validation bias and smaller errors than the second-order-only case (Burger et al., 2023).

Other non-Gaussian statistics were also applied to KiDS-1000. Density split statistics yielded

$ugriZYJHK_s$33

and were described as competitive with two-point cosmic shear while additionally constraining galaxy bias and shot-noise deviations (Burger et al., 2022). Peak count statistics obtained

$ugriZYJHK_s$34

in the KiDS-only analysis and $ugriZYJHK_s$35 in the combined KiDS-1000 and DES-Y1 analysis (Harnois-Deraps et al., 2024). A halo-model joint analysis of the stellar mass function, projected clustering, and galaxy-galaxy lensing found

$ugriZYJHK_s$36

demonstrating that small-scale clustering and galaxy-galaxy lensing can deliver constraints comparable to $ugriZYJHK_s$37pt analyses without including cosmic shear (Dvornik et al., 2022). A cluster-count and stacked weak-lensing analysis of about 8000 AMICO clusters reported

$ugriZYJHK_s$38

together with an average mass precision of $ugriZYJHK_s$39 for the $ugriZYJHK_s$40 relation (Lesci et al., 18 Jul 2025).

Analysis	Parameter	Representative result
Improved cosmic shear measurements	$ugriZYJHK_s$41	$ugriZYJHK_s$42
Multi-probe $ugriZYJHK_s$43pt	$ugriZYJHK_s$44	$ugriZYJHK_s$45
COSEBIs $ugriZYJHK_s$46	$ugriZYJHK_s$47	$ugriZYJHK_s$48
Density split statistics	$ugriZYJHK_s$49	$ugriZYJHK_s$50
Peak counts	$ugriZYJHK_s$51	$ugriZYJHK_s$52
AMICO clusters: counts + weak lensing	$ugriZYJHK_s$53	$ugriZYJHK_s$54

KiDS-1000 has also supported cross-correlation and model-building studies. The Planck CMB-lensing cross-correlation analysis used an intrinsic-alignment self-calibration method and obtained $ugriZYJHK_s$55 and $ugriZYJHK_s$56, while stressing the importance of boost-factor, cosmic-magnification, and photometric-redshift modelling (Yao et al., 2023). A model-agnostic reconstruction of the three-dimensional power spectrum found that a Planck-consistent reference spectrum requires $ugriZYJHK_s$57–$ugriZYJHK_s$58 suppression on non-linear scales to match KiDS-1000, whereas a lower-$ugriZYJHK_s$59 reference avoids suppression; the authors explicitly noted that this could indicate spurious systematic errors, inaccuracies in the intrinsic-alignment model, or potentially a non-standard cosmological model with delayed structure growth (Simon et al., 6 Feb 2025). At the methodological level, KiDS-1000 has further been used for map-level emulation with conditional generative adversarial networks (Yiu et al., 2021) and for accelerated constraints on Dark Scattering with ReACT and CosmoPower emulators (Carrion et al., 2024).

Taken together, these analyses show that KiDS-1000 is not a single cosmological measurement but a survey framework in which the same imaging and calibrated source sample support multiple estimators of late-time structure growth. A consistent pattern across the literature is that the dominant limitations are no longer purely statistical. Intrinsic alignments, baryonic feedback, redshift calibration, and forward-modelled observational anisotropies recur as the leading modelling issues, and several KiDS-1000 papers present specific methodological responses: improved SOM calibration, physical SED-based source characterization, MetaCalibration, equal-filter-radii compression for third-order statistics, and SBI with catalogue-level systematics (Busch et al., 2022, Halder et al., 3 Feb 2026, Yoon et al., 1 Oct 2025, Burger et al., 2023, Wietersheim-Kramsta et al., 2024).