KiDS-450: Testing extensions to the standard cosmological model

TL;DR

This study investigates whether extensions to LCDM can reconcile KiDS-450 weak-lensing tomography with Planck CMB measurements. Using extended lensing systematics and a suite of cosmological extensions (neutrino mass, curvature, constant and time-varying dark energy, modified gravity, and running of the spectral index), the authors assess parameter constraints, model fit via DIC, and cross-dataset concordance. They find that only a time-varying dark energy model (w0–wa) achieves substantial concordance between KiDS and Planck and is moderately favored when combining datasets, while other extensions largely fail to resolve the KiDS–Planck tension or are not favored by the data. KiDS constrains the sum of neutrino masses to <4 eV (95% CL) and shows no strong evidence for nonzero curvature or running; the results highlight the robustness of the S8 tension and emphasize the potential of evolving dark energy as a viable extension. The analysis underlines the importance of accurate nonlinear modeling (hmcode) and provides publicly available code and data for community use.

Abstract

We test extensions to the standard cosmological model with weak gravitational lensing tomography using 450 deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). In these extended cosmologies, which include massive neutrinos, nonzero curvature, evolving dark energy, modified gravity, and running of the scalar spectral index, we also examine the discordance between KiDS and cosmic microwave background measurements from Planck. The discordance between the two datasets is largely unaffected by a more conservative treatment of the lensing systematics and the removal of angular scales most sensitive to nonlinear physics. The only extended cosmology that simultaneously alleviates the discordance with Planck and is at least moderately favored by the data includes evolving dark energy with a time-dependent equation of state (in the form of the $w_0-w_a$ parameterization). In this model, the respective $S_8 = σ_8 \sqrt{Ω_{\rm m}/0.3}$ constraints agree at the $1σ$ level, and there is `substantial concordance' between the KiDS and Planck datasets when accounting for the full parameter space. Moreover, the Planck constraint on the Hubble constant is wider than in LCDM and in agreement with the Riess et al. (2016) direct measurement of $H_0$. The dark energy model is moderately favored as compared to LCDM when combining the KiDS and Planck measurements, and remains moderately favored after including an informative prior on the Hubble constant. In both of these scenarios, marginalized constraints in the $w_0-w_a$ plane are discrepant with a cosmological constant at the $3σ$ level. Moreover, KiDS constrains the sum of neutrino masses to 4.0 eV (95% CL), finds no preference for time or scale dependent modifications to the metric potentials, and is consistent with flatness and no running of the spectral index. The analysis code is public at https://github.com/sjoudaki/kids450

Figures (16)

• Figure 1: Ratio of shear correlation functions $\xi_{\pm}^{ij}(\theta)$ for tomographic bin combinations $\{1,4\}$ and $\{4,4\}$, taken for each extended parameter with respect to a flat $\Lambda$CDM model including no systematic uncertainties (denoted as $\xi_{\pm}[{\rm{fid}}]$). Parameter definitions are listed in Table \ref{['table:priors']}. For each perturbation, we keep all primary parameters fixed. These primary parameters include $\{\Omega_{\mathrm c}h^2, \Omega_{\mathrm b}h^2, \theta_{\mathrm{MC}}, \ln{(10^{10} A_{\mathrm s})}, n_{\mathrm s}\}$, along with the intrinsic alignment amplitude $A_{\rm IA}$ and baryon feedback amplitude $B$ when not explicitly varied (but not for instance the Hubble constant as it is a derived parameter). The curvature case corresponds to $\Omega_k = 0.01$, the neutrino mass case corresponds to $\sum m_{\nu} = 1~{\rm eV}$, and the case with nonzero running corresponds to ${{\mathrm d}n_{\mathrm s} / {\mathrm d}\ln k} = -0.1$. The modified gravity parameters Q and $\Sigma$ modify the gravitational constant and deflection of light, respectively. The dark energy equation of state can either be constant ($w$), or possess a time-dependence with $w_0$ and $w_a$. The shaded regions correspond to angular scales that are masked out in the KiDS analysis.
• Figure 2: Marginalized posterior contours in the $\sigma_8 - \Omega_{\mathrm m}$ plane (inner 68% CL, outer 95% CL). We show our fiducial KiDS constraints in green, KiDS with narrower priors on the Hubble constant and baryon density in grey (as in Hildebrandt16), KiDS with extended treatment of the astrophysical systematics in pink, and Planck in red.
• Figure 3: Marginalized posterior distributions of the lensing systematics parameters and their correlation. The vanilla parameters are simultaneously included in the analysis. We show KiDS with the fiducial treatment of systematic uncertainties in green (solid), and KiDS with the extended treatment of the lensing systematics in purple (dot-dashed). Parameter definitions and priors are listed in Table \ref{['table:priors']}.
• Figure 4: Marginalized posterior distributions for the intrinsic alignment amplitude considering different extended models.
• Figure 5: Left: Marginalized posterior contours in the $\sigma_8 - \Omega_{\mathrm m}$ plane (inner 68% CL, outer 95% CL) in a universe with massive neutrinos for KiDS in green and Planck in red. For comparison, dashed contours assume fiducial $\Lambda$CDM. Right: Marginalized posterior contours in the $\sum m_{\nu} - \Omega_{\mathrm m}$ plane for KiDS in green, KiDS with informative $H_0$ prior in grey (from riess16), and Planck in red.