KiDS-450 + 2dFLenS: Cosmological parameter constraints from weak gravitational lensing tomography and overlapping redshift-space galaxy clustering

TL;DR

The paper presents a joint analysis of KiDS-450 weak lensing tomography, galaxy-galaxy lensing, and redshift-space multipoles from overlapping 2dFLenS/BOSS data, using a self-consistent N-body covariance to extract cosmological and astrophysical constraints. By combining these observables, the authors tighten constraints along the lensing degeneracy, notably improving S_8 to 0.742 ± 0.035, while revealing a persistent 2.6–3.0σ discordance with Planck in ΛCDM and extended cosmologies. The analysis shows amplified IA amplitude constraints and stronger galaxy-bias determinations, and finds that modified gravity remains consistent with GR, with improved MG parameter limits when Planck data are included. Overall, the work demonstrates the power of multi-probe, overlapping surveys to sharpen cosmological inferences and MG tests, and provides CosmoLSS, a public toolkit for such analyses.

Abstract

We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg$^2$ of imaging data by the Kilo Degree Survey (KiDS) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of $N$-body simulations. We methodically analyze different combinations of the observables, finding that galaxy-galaxy lensing measurements are particularly useful in improving the constraint on the intrinsic alignment amplitude (by 30%, positive at $3.5σ$ in the fiducial data analysis), while the multipole power spectra are useful in tightening the constraints along the lensing degeneracy direction (e.g. factor of two stronger matter density constraint in the fiducial analysis). The fully combined constraint on $S_8 \equiv σ_8 \sqrt{Ω_{\rm m}/0.3} = 0.742 \pm 0.035$, which is an improvement by 20% compared to KiDS alone, corresponds to a $2.6σ$ discordance with Planck, and is not significantly affected by fitting to a more conservative set of scales. Given the tightening of the parameter space, we are unable to resolve the discordance with an extended cosmology that is simultaneously favored in a model selection sense, including the sum of neutrino masses, curvature, evolving dark energy, and modified gravity. The complementarity of our observables allows for constraints on modified gravity degrees of freedom that are not simultaneously bounded with either probe alone, and up to a factor of three improvement in the $S_8$ constraint in the extended cosmology compared to KiDS alone.

Figures (20)

• Figure 1: Overlapping imaging and spectroscopic surveys: dark squares are KiDS-450 pointings, and the fluctuating background is the gridded number density of 2dFLenS (blue) and BOSS (red) galaxies. The solid rectangles outline the footprint of the full KiDS survey.
• Figure 2: Measurements of the galaxy-galaxy lensing angular cross-correlation ($\gamma_{\rm t}$) for KiDS overlapping with 2dFLenS and BOSS against angular scale ($\theta$) in arcminutes. The grey regions denote angular scales that were removed from the cosmological analysis when employing fiducial cuts to the data (with conservative cuts, the measurements at 12 arcminutes were also removed for all tomographic bins). The open circles indicate negative values, and we have included best-fit theory lines in red (solid) for comparison.
• Figure 3: Measurements of the redshift-space multipole power spectra $\{P_0, P_2, P_4\}$ for 2dFLenS and BOSS in the overlap regions with KiDS at the bin mid-points $k = \{0.075, 0.125, 0.175\}~h~{\rm Mpc}^{-1}$. The grey regions denote physical scales that were removed from the cosmological analysis when employing fiducial cuts to the data (with conservative cuts, the measurements at $k = 0.125~h~{\rm Mpc}^{-1}$ were also removed for all galaxy samples). We have included best-fit theory lines in red (solid) for comparison.
• Figure 4: Correlation coefficients $r$ of the covariance matrix of the full data vector of cosmic shear, galaxy-galaxy lensing, and multipole power spectrum measurements for KiDS overlapping with 2dFLenS and BOSS (coefficients defined in equation \ref{['rcceqn']}). We show the elements of the $\{\xi_{\pm}, \gamma_{\rm t}, P_{0/2}\}$ data vector that were employed in the fiducial analysis (with selections detailed in Table \ref{['tabcuts']}). There are 130 elements of $\xi_{\pm}$, 64 elements of $\gamma_{\rm t}$, and 16 elements of $P_{0/2}$, delineated by thin solid lines. The $\gamma_{\rm t}$ and $P_{0/2}$ measurements are further delineated by thin dotted lines indicating the divisions between 2dFLOZ, 2dFHIZ, CMASS, and LOWZ. The ordering of the $\xi_{\pm}$ elements is the same as in our previous cosmic shear analyses (e.g. Heymans13joudaki16Hildebrandt16), where for 4 tomographic and 9 angular bins it follows $\{ \xi^{11}_+(\theta_1), \xi^{11}_+(\theta_2), ..., \xi^{11}_-(\theta_8), \xi^{11}_-(\theta_9), \xi^{12}_+(\theta_1), ..., \xi^{44}_-(\theta_9) \}$. We use a greyscale where white represents $r=-0.1$ and black represents $r=1$.
• Figure 5: Left: Marginalized posterior contours in the $\sigma_8$ -- $\Omega_{\mathrm m}$ plane (inner 68% CL, outer 95% CL) from $\{\xi_+, \xi_-\}$ in green, $\{\xi_+, \xi_-, \gamma_{\rm t}\}$ in purple, and $\{\xi_+, \xi_-, \gamma_{\rm t}\}$ with conservative cuts to the data in pink. For comparison, we show the constraints from Planck 2015 CMB temperature measurements in red. Right: Same as left panel, but with $\{\xi_+, \xi_-, P_0, P_2\}$ instead of $\{\xi_+, \xi_-, \gamma_{\rm t}\}$.