CFHTLenS: Combined probe cosmological model comparison using 2D weak gravitational lensing

TL;DR

This work uses CFHTLenS to perform a comprehensive 2D weak-lensing analysis, measuring ξ_± and E-/B-mode–separating statistics over 154 deg^2 with 4.2 million galaxies and robust photometric redshifts. It employs a cosmology-dependent covariance blending CFHTLenS clones with analytical Gaussian terms and uses Population Monte Carlo to fit non-linear power spectra with halofit, incorporating WMAP7, BOSS, and HST priors. The 2D lensing constraints on σ_8 and Ω_m yield σ_8(Ω_m/0.27)^{0.6} ≈ 0.79 ± 0.03, and, when combined with CMB/BAO/H_0 data, favor a flat ΛCDM cosmology with Ω_m ≈ 0.283 ± 0.010 and σ_8 ≈ 0.813 ± 0.014, while curved models are modestly disfavoured. Across different second-order estimators and robustness tests, the results remain consistent with ΛCDM, indicating no strong evidence for curvature or dynamic dark energy beyond the standard model.

Abstract

We present cosmological constraints from 2D weak gravitational lensing by the large-scale structure in the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) which spans 154 square degrees in five optical bands. Using accurate photometric redshifts and measured shapes for 4.2 million galaxies between redshifts of 0.2 and 1.3, we compute the 2D cosmic shear correlation function over angular scales ranging between 0.8 and 350 arcmin. Using non-linear models of the dark-matter power spectrum, we constrain cosmological parameters by exploring the parameter space with Population Monte Carlo sampling. The best constraints from lensing alone are obtained for the small-scale density-fluctuations amplitude sigma_8 scaled with the total matter density Omega_m. For a flat LambdaCDM model we obtain sigma_8(Omega_m/0.27)^0.6 = 0.79+-0.03. We combine the CFHTLenS data with WMAP7, BOSS and an HST distance-ladder prior on the Hubble constant to get joint constraints. For a flat LambdaCDM model, we find Omega_m = 0.283+-0.010 and sigma_8 = 0.813+-0.014. In the case of a curved wCDM universe, we obtain Omega_m = 0.27+-0.03, sigma_8 = 0.83+-0.04, w_0 = -1.10+-0.15 and Omega_K = 0.006+0.006-0.004. We calculate the Bayesian evidence to compare flat and curved LambdaCDM and dark-energy CDM models. From the combination of all four probes, we find models with curvature to be at moderately disfavoured with respect to the flat case. A simple dark-energy model is indistinguishable from LambdaCDM. Our results therefore do not necessitate any deviations from the standard cosmological model.

Figures (13)

• Figure 1: The redshift distribution $p(z_{\rm p})$ histogram, estimated as the sum of pdfs for $0.2 < z_{\rm p} < 1.3$ (thick red curve). For comparison, the histogram of the best-fitting photo-$z$s is shown as thin blue curve. Error bars correspond to the variance between the four Wide patches.
• Figure 2: Angles and coordinates on a sphere for two galaxies $i=1,2$ located at $(\alpha_i, \delta_i)$. Great circle segments are drawn as bold lines.
• Figure 3: Diagonal of the covariance $\textbfss{C}_{++}$ (top panel) and $\textbfss{C}_{--}$ (bottom), split up into various terms: Shot-noise $\textbfss{D}$ (solid red line), mixed term $\textbfss{M}$ (dashed green), cosmic variance $\textbfss{V}$ (dotted blue line and crosses) and shear calibration covariance $\textbfss{C}_m$ (see Sect. \ref{['sec:calib']}).
• Figure 4: Correlation coefficient of the total covariance, shot-noise plus mixed plus cosmic variance. The lower right triangle (within the red boundary) is the Gaussian prediction, the upper left (blue) triangle shows the total covariance with non-Gaussian parts from the Clone. The four blocks are $\textbfss{C}_{+-}, \textbfss{C}_{--}, \textbfss{C}_{++}$ and $\textbfss{C}_{-+}$, respectively, as indicated in the plot. The axes labels are the matrix indices $i$ and $j$.
• Figure 5: Trace of the covariance and inverse grafted cosmic covariance, plotted against the ratio of the number of bins $p$ to the number of realisations $n$. Shown are the cases for covariance (red squares), the inverse (green filled circles), and two cases where the inverse has been multiplied with the Anderson-Hartlap factor $\alpha$, corresponding to the number of bins $p=10$ (blue open circles), and $p=6$ (magenta triangles), causing an over-correction in both cases. This shows that we can use the inverse covariance estimator without correction (green curve).