Cosmological parameter constraints from galaxy-galaxy lensing and galaxy clustering with the SDSS DR7

TL;DR

This paper develops and applies a galaxy-galaxy lensing and clustering methodology to SDSS DR7 that removes small-scale halo physics via the annular differential surface density Υ, enabling robust constraints on matter clustering. By modeling a non-linear bias framework and using simulations to calibrate scale choices, it delivers competitive low-redshift measurements of σ8 and Ωm, with strong complementarity to CMB data. The analysis finds a tight constraint σ8(Ωm/0.25)^{0.57} ≈ 0.80 ± 0.05 from SDSS alone, which tightens substantially when combined with WMAP7, and provides meaningful bounds on neutrino masses and dark energy through joint cosmological fits. This approach offers a robust, relatively systematics-resistant avenue for current and future weak-lensing surveys to probe structure growth and cosmology.

Abstract

Recent studies have shown that the cross-correlation coefficient between galaxies and dark matter is very close to unity on scales outside a few virial radii of galaxy halos, independent of the details of how galaxies populate dark matter halos. This finding makes it possible to determine the dark matter clustering from measurements of galaxy-galaxy weak lensing and galaxy clustering. We present new cosmological parameter constraints based on large-scale measurements of spectroscopic galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We generalise the approach of Baldauf et al. (2010) to remove small scale information (below 2 and 4 Mpc/h for lensing and clustering measurements, respectively), where the cross-correlation coefficient differs from unity. We derive constraints for three galaxy samples covering 7131 sq. deg., containing 69150, 62150, and 35088 galaxies with mean redshifts of 0.11, 0.28, and 0.40. We clearly detect scale-dependent galaxy bias for the more luminous galaxy samples, at a level consistent with theoretical expectations. When we vary both σ_8 and Ω_m (and marginalise over non-linear galaxy bias) in a flat LCDM model, the best-constrained quantity is σ_8 (Ω_m/0.25)^{0.57}=0.80 +/- 0.05 (1-sigma, stat. + sys.), where statistical and systematic errors have comparable contributions, and we fixed n_s=0.96 and h=0.7. These strong constraints on the matter clustering suggest that this method is competitive with cosmic shear in current data, while having very complementary and in some ways less serious systematics. We therefore expect that this method will play a prominent role in future weak lensing surveys. When we combine these data with WMAP7 CMB data, constraints on σ_8, Ω_m, H_0, w_{de} and \sum m_ν become 30--80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.

Figures (26)

• Figure 1: Correlation function cross-correlation coefficient between mock LRGs and dark matter (data points) in the simulations described in Sec. \ref{['SS:simulations']}, with errors determined from the box to box variations in simulations. Lines are predictions from our model, with $r_\mathrm{cc}^{(\xi)}=1-(1/4)(b_2/b)^2 \xi_\text{lin}(r)$, using a large-scale bias of $b=2.07$ (selected to match the observed large-scale $\xi_{\mathrm{g}\mathrm{g}}$ and $\xi_{\mathrm{g}\mathrm{m}}$ in the mock LRG sample) and different values of $b_2$, with $b_2=0.5$ providing the best fit to the simulated clustering and lensing observable quantities. The plot goes to larger $r$ compared to the 2d values of $R$ used in our analysis, because the measured observables at some $R$ depend on the 3d correlation functions to larger $r$.
• Figure 2: Top: $\Upsilon_\text{gm}$ for mock LRGs and the model predictions. Bottom: $\Upsilon_\text{gg}$ for mock LRGs and the model predictions.
• Figure 3: Area coverage of the lens samples used in this paper.
• Figure 4: Top: Redshift distribution $\mathrm{d} p/\mathrm{d} z$ for the three lens samples used in this work, as labeled on the plot. The solid and dashed lines show the unweighted and weighted histograms, respectively. Bottom: Comoving number density $\bar{n}$, in units of $10^{-4}(h/\text{Mpc})^3$ (multiplied by $0.1$ for Main-L5 for easier viewing). The dotted vertical lines show the delineation between the different lens samples.
• Figure 5: Histograms of source galaxy properties, derived from a random subsample of 5 per cent of the catalogue after imposing all cuts ($\sim 2\times 10^{6}$ galaxies). Top: Histogram of $r$-band extinction corrected model magnitude. Bottom: photo-$z$ histogram, and the inferred true $\mathrm{d} N/\mathrm{d} z$ from N12.