Galaxy Clustering

Sixty published galaxy clustering measurements catalogued in literature_measurements/clustering/, organised by statistic. The collection covers seven two-point statistics: wprp (projected correlation function), wtheta (angular correlation function), xi_multipoles (redshift-space multipoles), Pk (galaxy power spectrum), Pk_multipoles (power spectrum multipoles), DeltaSigma (excess surface mass density), and cosmic_shear (shear–shear correlations). Each entry has a paper.json with full provenance (survey, method, cosmology, key results per redshift bin).

Conventions: projected correlation function wₚ(rₚ) is in h⁻¹ Mpc; power spectra P(k) in (h⁻¹ Mpc)³; fsigma8 is the growth-rate amplitude. H₀ = 100 h km s⁻¹ Mpc⁻¹ throughout.

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Measurement methods

Projected correlation function wₚ(rₚ)

The projected correlation function integrates the 2D redshift-space correlation function ξ(rₚ, π) along the line-of-sight separation π, suppressing the effect of peculiar velocities (redshift-space distortions):

\[w_p(r_p) = 2 \int_0^{\pi_{\max}} \xi(r_p, \pi)\,\mathrm{d}\pi\]

where rₚ is the transverse (projected) separation and πmax is the integration limit, chosen large enough to include all correlated pairs (typically 40–100 h⁻¹ Mpc).

The Landy-Szalay estimator for ξ(rₚ, π) is:

\[\hat{\xi}(r_p, \pi) = \frac{DD - 2\,DR + RR}{RR}\]

where DD, DR, and RR are the normalised data-data, data-random, and random-random pair counts. The key advantage over the angular or redshift-space correlation function is that wₚ is insensitive to linear RSD, enabling clean HOD modelling on small scales.

Key code: sum_stat.twopcf.projected. Reference: Davis & Peebles 1983, ApJ 267, 465.

Angular correlation function w(θ)

The angular two-point correlation function is measured in projected angular separation θ without any redshift information:

\[\hat{w}(\theta) = \frac{DD(\theta) - 2\,DR(\theta) + RR(\theta)}{RR(\theta)}\]

(Landy-Szalay estimator projected on the sky). No photo-z accuracy is needed, making it the natural statistic for photometric surveys such as DES and SDSS commissioning. The Limber approximation connects w(θ) to the 3D matter power spectrum P_m(k) through the redshift distribution n(z) of the sample.

Key code: sum_stat.twopcf.angular.

Redshift-space multipoles ξ_ℓ(s)

The redshift-space correlation function can be decomposed into Legendre multipoles:

\[\xi(s, \mu) = \sum_\ell \xi_\ell(s)\,\mathcal{L}_\ell(\mu)\]

where s is the redshift-space separation, μ = cos θ is the cosine of the angle to the line of sight, and ℓ = 0, 2, 4 are the monopole, quadrupole, and hexadecapole. In the linear (Kaiser 1987) limit:

\[\frac{\xi_2}{\xi_0} = \frac{\tfrac{4}{3}\beta + \tfrac{4}{7}\beta^2} {1 + \tfrac{2}{3}\beta + \tfrac{1}{5}\beta^2}\]

where β = f/b is the ratio of the linear growth rate f to the linear galaxy bias b. The multipoles encode both RSD (growth rate fσ₈) and BAO (the standard ruler from the baryon acoustic oscillation in the matter power spectrum).

Key code: sum_stat.twopcf.multipoles. References: Kaiser 1987, MNRAS 227, 1; Hamilton 1992, ApJ 385, L5.

Power spectrum P(k)

The galaxy power spectrum is estimated as the Fourier transform of the density field:

\[\hat{P}(k) = \frac{|\delta_k|^2}{V}\]

where \(\delta_k\) are the Fourier modes of the galaxy overdensity field δ(r) = n(r)/n̄ − 1 and V is the survey volume. In practice, window function deconvolution is required to correct for the survey geometry, and FKP weighting (Feldman, Kaiser & Peacock 1994) is applied to optimise the signal-to-noise:

\[w(\mathbf{r}) = \frac{1}{1 + \bar{n}(\mathbf{r})\,P_0}\]

where P₀ is a reference power spectrum amplitude and n̄(r) is the expected mean galaxy density.

Key code: sum_stat.powspec.pk3d. Reference: Feldman, Kaiser & Peacock 1994, ApJ 426, 23.

Power spectrum multipoles P_ℓ(k)

As with the correlation function, the anisotropic power spectrum can be decomposed into Legendre multipoles P₀(k), P₂(k), P₄(k). This captures both RSD and BAO simultaneously in a single compressed statistic.

Modelling is performed with the Effective Field Theory of Large Scale Structure (EFTofLSS; Perko et al. 2016; Ivanov+2020) or the TNS model (Taruya, Nishimichi & Saito 2010) for the non-linear power spectrum. The EFT approach has become the standard for BOSS DR12 and DESI DR1 full-shape analyses.

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Status and open questions

Large-scale growth rate

On large scales (s > 20 h⁻¹ Mpc, k < 0.1 h Mpc⁻¹), the linear growth rate fσ₈(z) is now measured to 2–3% precision from the combination of BOSS DR12 + eBOSS across 0 < z < 2.4 (Alam+2021). The combined constraints are consistent with general relativity (GR) to ~5%, providing one of the most stringent tests of gravity on cosmological scales. DESI DR1 (2024) extends this to 6 galaxy tracers spanning 0.1 < z < 2.33, with fσ₈ constraints that will eventually surpass BOSS at all redshifts.

Small-scale clustering and baryonic effects

On small scales (rₚ < 1 h⁻¹ Mpc, the 1-halo term), galaxy clustering measurements from different surveys show 10–30% discrepancies. The main culprits are:

• Fiber collisions: SDSS and BOSS fibers cannot be placed within 55 arcsec of each other, causing correlated losses of pairs at small separations. Correction methods (angular upweighting, nearest-neighbour assignments) have 5–15% residual uncertainty.

• Baryonic feedback: supernova- and AGN-driven winds modify halo profiles and the satellite distribution on scales < 1 Mpc, causing deviations from DMO predictions at the 10–30% level.

• Photometric scatter: stellar mass estimates carry ~0.15–0.2 dex scatter, which smooths out the clustering signal across stellar mass bins.

Assembly bias

Galaxies with the same halo mass but different halo formation histories (concentration, spin, formation time) cluster differently, a phenomenon known as assembly bias (Gao, Springel & White 2005). Standard HOD models assume clustering depends only on halo mass, and ignoring assembly bias introduces a systematic error of ~10–20% in the inferred SMHM relation. Assembly bias has been detected at ~2–3σ in SDSS (e.g., Lacerna+2022, Xu & Zheng 2020) and is a potential systematic in all HOD-based analyses, including DESI BGS.

Galaxy-halo connection evolution

The scatter in the SMHM relation (σ_SMHM ~ 0.15–0.20 dex) is well constrained locally from joint wp + ΔΣ analyses (Zu & Mandelbaum 2015). However, its evolution with redshift is uncertain at the 20–30% level above z ~ 0.5, because deep spectroscopic surveys with sufficient volume and clustering signal-to-noise at z > 0.5 are just now becoming available (VIPERS, eBOSS, DESI).

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Progress over two decades

• 2002–2003: 2dFGRS (Cole+2005, Norberg+2002) and SDSS (Tegmark+2004, Blanton+2003) produce the first precise measurements of P(k) shape and wₚ(rₚ) at z ~ 0. The BAO feature in the galaxy power spectrum is detected at ~2σ by Eisenstein+2005 (SDSS LRG). The HOD emerges as the standard framework for interpreting small-scale clustering (Zehavi+2004/2005).

• 2005: Zehavi+2005 (SDSS DR3) establishes the HOD as the community standard for galaxy–halo connection inference from wₚ(rₚ).

• 2008: Guzzo+2008 (VVDS, Nature) report the first high-z RSD measurement in Nature at z ~ 0.77, showing that RSD can distinguish between dark energy and modified gravity.

• 2011–2012: BOSS DR7/DR11 (Anderson+2012) and WiggleZ (Blake+2011) deliver BAO distance measurements to 1–3% precision and fσ₈ to ~10%.

• 2014–2017: BOSS DR11/DR12 gold standard — Anderson+2014, Samushia+2014, Alam+2017 — delivers BAO to 1% and fσ₈ to 4% at z = 0.32 and z = 0.57, representing the state-of-the-art for clustering cosmology for nearly a decade.

• 2020–2021: eBOSS DR16 full-shape analyses with EFTofLSS (Ivanov+2020, Philcox & Ivanov 2022) combine BAO + RSD + full-shape P(k) for combined σ₈ and H₀ constraints.

• 2024: DESI DR1 (5.7M galaxy BAO; Adame+2024) is the largest galaxy clustering dataset, delivering BAO at 6× the statistical power of BOSS across 7 tracers. First full-shape EFTofLSS at DESI precision (Adame+2025).

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Survey parameter table

Survey	Statistic	z range	Area (deg²)	Ngal	Veff (h-3 Gpc³)	n̄ (10⁻⁴ h³ Mpc⁻³)
2dFGRS	wprp + Pk	0 – 0.3	2000	220 k	0.04	5.5
SDSS_DR7	wprp + Pk	0 – 0.22	7000	200 k	0.5	0.4
BOSS_LOWZ	wprp + ξ	0.15 – 0.43	9000	250 k	0.5	0.5
BOSS_CMASS	ξ + Pk	0.43 – 0.70	9000	690 k	1.5	0.46
eBOSS_LRG	ξ	0.6 – 1.0	7500	174 k	1.8	0.1
eBOSS_ELG	ξ	0.6 – 1.1	1000	174 k	0.9	0.19
eBOSS_QSO	ξ	0.8 – 2.2	7500	344 k	4.6	0.075
DESI_DR1	ξ + Pk	0.1 – 2.1	9000	5700 k	18	various

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Figures

Growth rate fσ₈(z) from all RSD measurements. Grey band: GR prediction (Planck 2018). Points from 2dFGRS, 6dFGS, VVDS, WiggleZ, BOSS LOWZ/CMASS, eBOSS LRG/ELG/QSO, and DESI DR1. (Figure will appear here once the figure script has been run.)

Effective volume V_eff vs mean number density n̄ for galaxy clustering surveys. Symbol size is proportional to √N_gal. (Figure will appear here once the figure script has been run.)

Growth rate fσ₈(z) compiled from 2dFGRS, WiggleZ, BOSS, eBOSS, and DESI.

BAO distance ratio D_V/r_d (and D_M/r_d, D_H/r_d) vs redshift from 6dFGS, SDSS, BOSS, eBOSS, and DESI. (Figure will appear here once the figure script has been run.)

Projected clustering length r₀ vs redshift from wprp measurements spanning 2dFGRS, SDSS, BOSS, VIPERS, and DEEP2.

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Projected correlation function wₚ(rₚ)

Thirteen entries measuring the projected two-point correlation function by integrating along the line-of-sight to suppress redshift-space distortions. Several entries (More 2015, More 2023, Zu & Mandelbaum 2015/2016, DESI 2025) include joint wp(rp) + DeltaSigma analyses and appear also in the DeltaSigma section below.

Directory / ID	Survey	z range	Ngal	Key result	Cites
SDSS_Zehavi2011	SDSS DR7 spec-z	0.02 – 0.22	200 k	r₀=5.45 h⁻¹ Mpc, γ=1.88; HOD per luminosity bin	~1200
2dFGRS_Norberg2002	2dFGRS spec-z	0.01 – 0.30	96 k	r₀=5.1 h⁻¹ Mpc; relative bias b/b★ vs luminosity	~400
BOSS_Guo2015	BOSS DR11 LOWZ+CMASS spec-z	0.15 – 0.70	760 k	r₀=8.5 (LOWZ), 7.0 (CMASS) h⁻¹ Mpc; HOD + SHAM	~200
VIPERS_Marulli2013	VIPERS PDR-1 spec-z	0.50 – 1.10	31 k	r₀=5.4 h⁻¹ Mpc, b~1.4 at z~0.8; luminosity dependence	~130
VVDS_Abbas2010	VVDS wide+deep spec-z	0.50 – 1.20	7.7 k	r₀=3.75 h⁻¹ Mpc, γ=1.70 at z~0.7; luminosity dependence	~100
zCOSMOS_Meneux2009	zCOSMOS bright 10k spec-z	0.20 – 1.00	10.6 k	r₀=3.5–3.0 h⁻¹ Mpc (z=0.35–0.85); mass+luminosity dependence	~170
DEEP2_Coil2006	DEEP2 spec-z	0.75 – 1.35	11 k	r₀=4.0 h⁻¹ Mpc, γ=1.65 at z~1; red/blue galaxy split	~250
SDSS_Zheng2007	SDSS DR5 spec-z	0.02 – 0.22	170 k	r₀=5.36 h⁻¹ Mpc, γ=1.84; HOD per luminosity bin; SDSS+DEEP2+COMBO-17 HOD evolution	~400
SDSS_More2015_wprp	BOSS DR11 x CFHTLenS	0.16 – 0.70	560 k	Joint wp(rp)+DeltaSigma+abundance HOD; Omega_m=0.310, sigma8=0.785	~152
SDSS_More2023_wprp	BOSS DR12 x HSC Y3	0.15 – 0.70	730 k	wp(rp) for LOWZ/CMASS/CMASS-ELG; 12 log bins 0.1–60 h⁻¹ Mpc; HSC Y3 3x2pt	~67
SDSS_ZuMandelbaum2015_wprp	SDSS DR7 spec-z	0.02 – 0.30	150 k	iHOD joint wp(rp)+DeltaSigma+SMF; SMHM scatter 0.18–0.22 dex; 4 stellar mass bins	~186
SDSS_ZuMandelbaum2016_wprp	SDSS DR7 spec-z	0.02 – 0.30	150 k	iHOD red/blue split; halo quenching threshold M_h ~ 1.5×10¹² h⁻¹ M☉	~130
DESI_2025_wprp	DESI DR1 BGS+LRG x HSC/KiDS/DES/SDSS	0.1 – 0.8	—	First DESI DR1 wp(rp) for BGS and LRG; joint wprp+DeltaSigma measurement	~12

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Angular correlation function w(θ)

Three entries measuring the angular two-point correlation function in photometric redshift slices.

Directory / ID	Survey	z range	Ngal	Key result	Cites
DES_ElvinPoole2018	DES Y1 redMaGiC photo-z	0.15 – 0.90	660 k	bias b=1.45–2.00 in 5 photo-z bins; DES Y1 3×2pt component	~600
DES_RodriguezMonroy2022	DES Y3 MagLim photo-z	0.20 – 1.05	10.7 M	bias b=1.41–2.07 in 6 photo-z bins; SYSnet systematics; DES Y3 3x2pt	~110
SDSS_Scranton2002	SDSS commissioning photo-z	0.10 – 0.40	1.4 M	A~0.01, δ=0.77; Γ~0.17; scale-dependent bias detected	~200
2dFGRS_Blake2002	2dFGRS photometric parent	0.00 – 0.60	100 k	A~0.02, δ=0.70 in 6 photo-z slices; angular BAO hint >2σ	~200

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Redshift-space multipoles ξ_ℓ(s)

Thirteen entries measuring the monopole, quadrupole (and hexadecapole) of the two-point correlation function in redshift space, used for RSD and BAO analyses.

Directory / ID	Survey	z range	Ngal	Key result	Cites
2dFGRS_Hawkins2003	2dFGRS spec-z	0.00 – 0.30	160 k	β=0.49±0.09, r₀=5.05 h⁻¹ Mpc, σ_v=506 km/s at z~0.15	~1000
2dFGRS_Percival2004	2dFGRS spec-z	0.00 – 0.30	220 k	β=0.58±0.08 at z~0.17; first precision RSD from spherical harmonics decomposition	~400
6dFGS_Beutler2012	6dF Galaxy Survey spec-z	0.00 – 0.25	75 k	BAO DV(z=0.106)/rs=0.336±0.015 (4.5%); lowest-z BAO detection at 2.4σ	~800
VVDS_Guzzo2008	VVDS spec-z	0.60 – 1.20	11.6 k	f(z=0.77)=0.91±0.36, β=0.70; first high-z RSD measurement	~650
WiggleZ_Blake2011	WiggleZ spec-z	0.10 – 0.90	153 k	fsigma8=0.454, 0.430, 0.418, 0.290 at z=0.22–0.78	~700
BOSS_Anderson2014	BOSS DR11 LOWZ+CMASS spec-z	0.20 – 0.70	690 k	BAO DV/rd to 2% precision at z=0.32 and z=0.57; anisotropic BAO DM/rd+DH/rd	~1100
BOSS_Samushia2014	BOSS DR11 CMASS spec-z	0.43 – 0.70	690 k	fsigma8=0.441±0.044 at z=0.57; DV/rd=13.50±0.22	~600
BOSS_Ross2017	BOSS DR12 LOWZ spec-z	0.15 – 0.43	362 k	BAO DV/rd=8.47±0.17 at z=0.32 from post-reconstruction xi(s); companion to Alam+2017	~500
BOSS_Alam2017	BOSS DR12 LOWZ+CMASS spec-z	0.20 – 0.75	1.20 M	fsigma8=0.427 (z=0.32), 0.426 (z=0.57); BAO α⊥, α‖	~3000
eBOSS_Bautista2021	eBOSS DR16 LRG spec-z	0.60 – 1.00	175 k	fsigma8=0.473±0.044 at z=0.698; DM/rd=17.65, DH/rd=19.77	~200
eBOSS_deMattia2021	eBOSS DR16 ELG spec-z	0.60 – 1.10	174 k	fsigma8=0.289±0.096 at z=0.845; DM/rd=18.33, DH/rd=20.0	~100
eBOSS_Neveux2020	eBOSS DR16 QSO spec-z	0.80 – 2.20	344 k	fsigma8=0.462±0.045 at z=1.48; DM/rd=30.21, DH/rd=13.23	~150
DESI_2024_xi	DESI DR1 (EDR) BGS+LRG+ELG+QSO+Lyα	0.10 – 2.33	5.7 M	BAO DM/rd+DH/rd for 7 tracers; BGS(0.295), LRG1–3, ELG1–2, QSO, Lyα	~1000
DESI_2024_twopoint	DESI DR1 (Year 1) all tracers	0.10 – 2.10	6.0 M	Two-point statistics (ξ multipoles + Pk multipoles) for all 6 DESI DR1 tracers; feeds full-shape analysis	~110

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Galaxy power spectrum P(k)

Three entries measuring the galaxy power spectrum shape (no multipoles), primarily constraining Ω_mh and the BAO scale.

Directory / ID	Survey	z range	Ngal	Key result	Cites
SDSS_Tegmark2004	SDSS DR1 spec-z	0.02 – 0.30	205 k	Ω_m·h=0.213±0.023; P(k) shape from first SDSS DR1 data	~1800
2dFGRS_Cole2005	2dFGRS spec-z	0.00 – 0.30	220 k	Ω_m·h=0.168±0.016, f_b=0.185±0.046; final 2dFGRS P(k)	~700
SDSS_Percival2010	SDSS DR7 (main+LRG) spec-z	0.00 – 0.50	893 k	DV(z=0.275)/rs=0.1390±0.0037; BAO at 3.6% precision	~1500

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Power spectrum multipoles P_ℓ(k)

Six entries using the full-shape power spectrum multipoles P₀+P₂(+P₄) with EFT or TNS models for joint BAO + RSD constraints.

Directory / ID	Survey	z range	Ngal	Key result	Cites
BOSS_GilMarin2016	BOSS DR12 LOWZ+CMASS spec-z	0.20 – 0.75	1.20 M	fsigma8=0.497 (z=0.32), 0.422 (z=0.57); P_ℓ + bispectrum	~350
BOSS_Beutler2017	BOSS DR12 LOWZ+CMASS spec-z	0.20 – 0.75	1.20 M	fsigma8=0.396 (z=0.32), 0.417 (z=0.57); P₀+P₂+P₄ TNS model	~600
BOSS_Ivanov2020	BOSS DR12 LOWZ+CMASS spec-z	0.20 – 0.75	1.20 M	Ω_m=0.311±0.025, H₀=67.9±1.1, σ₈=0.721±0.043; EFTofLSS	~400
BOSS_PhilcoxIvanov2022	BOSS DR12 LOWZ+CMASS spec-z	0.20 – 0.75	1.20 M	BOSS DR12 P0+P2+B0 EFTofLSS; H₀=69.6, σ₈=0.692, S8=0.751±0.039	~279
DESI_2024_Pk	DESI DR1 (EDR) LRG+ELG+QSO	0.40 – 2.10	—	P₀+P₂+P₄ for 4 tracers; ShapeFit + EFTofLSS full-shape	~500
DESI_2024_fullshape	DESI DR1 (Year 1) all tracers	0.10 – 2.10	4.7 M	Full-shape P0+P2+P4; Ω_m=0.296±0.010, H₀=68.63±0.79, σ₈=0.841±0.034	~157
DESI_2024_fullshape_cosmo	DESI DR1 (Year 1) all tracers	0.10 – 2.10	4.7 M	Cosmological constraints from full-shape DESI DR1; DESI 2024 VII flagship cosmology paper	~293

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Excess surface mass density ΔΣ(R)

These measurements use galaxy–galaxy lensing to measure the excess surface mass density ΔΣ(R) = Σ_cr γ_t around spectroscopic lens galaxies. Several analyses combine ΔΣ with wp(rp) for joint HOD or halo model constraints on cosmological parameters (S8, Ω_m).

Note

ΔΣ(R) entries that also appear in the wprp section (More 2015, More 2023, Zu & Mandelbaum 2015/2016, DESI 2025) share the same ADS bibcode and paper.json with their wprp counterparts — the measurement paper covers both statistics.

Directory / ID	Survey	z range	Ngal	Key result	Cites
SDSS_Mandelbaum2006	SDSS DR4 spec-z	0.02 – 0.35	300 k	Halo masses M200b for L1–L6 luminosity bins; luminosity–halo mass relation	~500
COSMOS_Leauthaud2012	COSMOS (HST ACS)	0.20 – 1.00	120 k	First joint SMF+DeltaSigma+wp HOD 0.2<z<1.0; SMHM evolution; n_eff~66 arcmin⁻²	~700
SDSS_ZuMandelbaum2015	SDSS DR7 spec-z	0.02 – 0.30	150 k	DeltaSigma for 4 stellar mass bins; iHOD SMHM scatter 0.18–0.22 dex	~186
SDSS_ZuMandelbaum2016	SDSS DR7 spec-z	0.02 – 0.30	150 k	DeltaSigma red/blue subsamples; halo quenching threshold M_h ~ 1.5×10¹² h⁻¹ M☉	~130
SDSS_Mandelbaum2016	SDSS DR7 spec-z	0.02 – 0.20	50 k	Halo mass bimodality: red centrals ~0.5 dex more massive than blue at fixed M★	~130
SDSS_More2015	BOSS DR11 x CFHTLenS	0.16 – 0.70	560 k	DeltaSigma for BOSS LOWZ+CMASS; HOD fit yields Ω_m=0.310, σ₈=0.785	~152
DES_Prat2018	DES Y1 redMaGiC	0.15 – 0.90	660 k	DeltaSigma for 5 lens bins × 4 source bins; b=1.45–2.00; DES Y1 3x2pt	~270
HSC_Miyatake2022	HSC Y1 x BOSS	0.15 – 0.70	430 k	DeltaSigma for BOSS LOWZ+CMASS x HSC Y1; S8=0.795+0.049-0.042; ~1.5σ below Planck	~130
KiDS_Heymans2021	BOSS DR12 x KiDS-1000 (3x2pt)	0.15 – 0.75	1.0 M	S8=0.766+0.020-0.014 (~2.7σ below Planck) from BOSS w(θ)+DeltaSigma+KiDS shear	~600
KiDS_Dvornik2022	KiDS-1000 bright galaxies	0.10 – 0.90	1.0 M	DeltaSigma for KiDS bright luminosity/stellar mass bins; 0.05–2 Mpc; HOD+wp joint fit	~60
DES_Pandey2022	DES Y3 redMaGiC	0.20 – 0.65	—	DES Y3 2x2pt redMaGiC; S8~0.78; 5 lens bins; clustering + galaxy-galaxy lensing	~116
DES_Prat2022	DES Y3 MagLim	0.20 – 1.05	10.7 M	DeltaSigma for 6 MagLim lens bins × 4 source bins; DES Y3 3x2pt S8=0.776	~150
HSC_More2023	HSC Y3 x BOSS DR12	0.15 – 0.70	730 k	DeltaSigma for 3 BOSS lens samples × 4 HSC Y3 source bins; 416 deg²; 12 measurement vectors	~67
HSC_Miyatake2023	HSC Y3 x BOSS DR12	0.15 – 0.70	—	3x2pt emulator halo model; S8=0.763±0.036 (~2.5σ below Planck)	~120
HSC_Sugiyama2023	HSC Y3 x BOSS DR12	0.15 – 0.70	—	3x2pt perturbation theory minimal bias; S8=0.775+0.043-0.038; consistent with Planck	~124
SDSS_More2023	BOSS DR12 x HSC Y3	0.15 – 0.70	730 k	DeltaSigma for LOWZ/CMASS/CMASS-ELG x 4 HSC Y3 source bins; 416 deg²; 12 log bins	~67
DESI_2025_GGL	DESI DR1 BGS+LRG x HSC/KiDS/DES/SDSS	0.1 – 0.8	—	First DESI DR1 DeltaSigma for BGS and LRG; cross-survey consistency of GGL signal	~12

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Cosmic shear γγ

Two entries measuring shear–shear (γγ) correlations that appear in the clustering index. For the complete catalogue of Stage-III cosmic shear measurements (10 entries: CFHTLenS, KiDS-450, KiDS-1000, DES Y1/Y3, HSC Y1/Y3) with S8 constraints and shear estimator details, see Cosmic Shear.

Note

These are pure γγ (shear–shear) measurements, not lens–source (galaxy–galaxy lensing). The KiDS_Wright2025 entry is the final KiDS Legacy release (complete survey footprint), giving a notably higher S8 than earlier KiDS releases.

Directory / ID	Survey	z range	Nsrc	Key result	Cites
KiDS_Asgari2021	KiDS-1000 shear	0.1 – 1.2	21 M	S8=0.759+0.024-0.021 (~3σ below Planck); band powers + COSEBIs; companion to Heymans+2021	~771
KiDS_Wright2025	KiDS-Legacy (final release)	0.1 – 1.2	—	S8=0.81+0.016-0.021 — notably higher than earlier KiDS releases; consistent with Planck	~206

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Summary figures

S8 = σ₈(Ω_m/0.3)^0.5 constraints from Stage-III lensing surveys (KiDS, DES, HSC) compared to Planck 2018.