.. _literature_clustering: 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. .. contents:: On this page :local: :depth: 1 ---- 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): .. math:: 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: .. math:: \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: .. math:: \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: .. math:: \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: .. math:: \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: .. math:: \hat{P}(k) = \frac{|\delta_k|^2}{V} where :math:`\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: .. math:: 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. ---- 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). ---- 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). ---- Survey parameter table ----------------------- .. list-table:: :header-rows: 1 :widths: 20 14 10 9 9 14 11 * - Survey - Statistic - z range - Area (deg²) - N\ :sub:`gal` - V\ :sub:`eff` (h\ :sup:`-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 ---- Figures ------- .. figure:: ../figures/literature/lit_clustering_fsgma8.png :width: 80% :alt: Growth rate fσ₈(z) compilation 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.)* .. figure:: ../figures/literature/lit_clustering_survey_coverage.png :width: 70% :alt: Effective volume vs number density 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.)* .. figure:: ../figures/literature/fsigma8_vs_z.png :alt: Growth rate compilation :width: 80% Growth rate fσ₈(z) compiled from 2dFGRS, WiggleZ, BOSS, eBOSS, and DESI. .. figure:: ../figures/literature/bao_DV_rd_vs_z.png :alt: BAO distance compilation :width: 80% 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.)* .. figure:: ../figures/literature/clustering_r0_vs_z.png :alt: Clustering length r0 vs z :width: 80% Projected clustering length r₀ vs redshift from wprp measurements spanning 2dFGRS, SDSS, BOSS, VIPERS, and DEEP2. ---- 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 :ref:`DeltaSigma section ` below. .. list-table:: :header-rows: 1 :widths: 28 22 9 7 25 9 * - Directory / ID - Survey - z range - N\ :sub:`gal` - 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 ---- Angular correlation function w(θ) ---------------------------------- Three entries measuring the angular two-point correlation function in photometric redshift slices. .. list-table:: :header-rows: 1 :widths: 28 24 9 7 23 9 * - Directory / ID - Survey - z range - N\ :sub:`gal` - 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 ---- Redshift-space multipoles ξ\ :sub:`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. .. list-table:: :header-rows: 1 :widths: 28 22 9 7 25 9 * - Directory / ID - Survey - z range - N\ :sub:`gal` - 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 ---- Galaxy power spectrum P(k) -------------------------- Three entries measuring the galaxy power spectrum shape (no multipoles), primarily constraining Ω\ :sub:`m`\ h and the BAO scale. .. list-table:: :header-rows: 1 :widths: 28 22 9 7 25 9 * - Directory / ID - Survey - z range - N\ :sub:`gal` - 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 ---- Power spectrum multipoles P\ :sub:`ℓ`\ (k) -------------------------------------------- Six entries using the full-shape power spectrum multipoles P₀+P₂(+P₄) with EFT or TNS models for joint BAO + RSD constraints. .. list-table:: :header-rows: 1 :widths: 28 22 9 7 25 9 * - Directory / ID - Survey - z range - N\ :sub:`gal` - 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 ---- .. _lit_clust_deltasigma: Excess surface mass density ΔΣ(R) ----------------------------------- These measurements use galaxy–galaxy lensing to measure the excess surface mass density ΔΣ(R) = Σ\ :sub:`cr` γ\ :sub:`t` around spectroscopic lens galaxies. Several analyses combine ΔΣ with wp(rp) for joint HOD or halo model constraints on cosmological parameters (S8, Ω\ :sub:`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. .. list-table:: :header-rows: 1 :widths: 28 22 9 7 25 9 * - Directory / ID - Survey - z range - N\ :sub:`gal` - 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`_ - 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 ---- 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 :ref:`literature_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. .. list-table:: :header-rows: 1 :widths: 28 24 9 7 23 9 * - Directory / ID - Survey - z range - N\ :sub:`src` - 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 ---- Summary figures --------------- .. figure:: ../figures/literature/s8_compilation.png :alt: S8 tension :width: 80% S8 = σ₈(Ω_m/0.3)^0.5 constraints from Stage-III lensing surveys (KiDS, DES, HSC) compared to Planck 2018.