Cosmic Discordance: Are Planck CMB and CFHTLenS weak lensing measurements out of tune?

TL;DR

This work rigorously tests the agreement between Planck+WP CMB measurements and CFHTLenS weak-lensing data within the base ΛCDM model and several extensions. By reanalyzing CFHTLenS with full tomographic information, marginalizing over intrinsic alignments and baryonic effects, and evaluating multi-dimensional parameter space via iso-likelihoods, it provides a robust measure of tension. In ΛCDM the datasets remain discrepant; massive active neutrinos do not resolve the discordance, while a sterile neutrino can improve overlap but does not definitively reconcile them, with ΔN_eff ≈ 0.82 being favored under joint fits. The study offers updated CFHTLenS fitting functions and highlights the potential need for new physics or unidentified systematics, guiding future joint analyses of CMB and weak lensing data.

Abstract

We examine the level of agreement between low redshift weak lensing data and the CMB using measurements from the CFHTLenS and Planck+WMAP polarization. We perform an independent analysis of the CFHTLenS six bin tomography results of Heymans et al. (2013). We extend their systematics treatment and find the cosmological constraints to be relatively robust to the choice of non-linear modeling, extension to the intrinsic alignment model and inclusion of baryons. We find that the 90% confidence contours of CFHTLenS and Planck+WP do not overlap even in the full 6-dimensional parameter space of $Λ$CDM, so the two datasets are discrepant. Allowing a massive active neutrino or tensor modes does not significantly resolve the disagreement in the full n-dimensional parameter space. Our results differ from some in the literature because we use the full tomographic information in the weak lensing data and marginalize over systematics. We note that adding a sterile neutrino to $Λ$CDM does bring the 8-dimensional 64% contours to overlap, mainly due to the extra effective number of neutrino species, which we find to be 0.84 $\pm$ 0.35 (68%) greater than standard on combining the datasets. We discuss why this is not a completely satisfactory resolution, leaving open the possibility of other new physics or observational systematics as contributing factors. We provide updated cosmology fitting functions for the CFHTLenS constraints and discuss the differences from ones used in the literature.

Figures (9)

• Figure 1: The Planck and CFHTLenS data superposed onto the present day matter power spectrum, using the method of tegmark02. Each coloured CFHTLenS point corresponds to an angular correlation function measurement. Cross correlations with tomographic bin 1 are magenta, with bin 2 (and not with bin 1) are red, with bin 3 (and not with bins 1 or 2) are yellow, bin 4 are green, bin 5 are cyan and bin 6 are blue. There are 105 points from CFHTLenS $\xi_{+}$ which are illustrated by the coloured points. Some of them fall at smaller scales than shown on this plot, and some are negative and shown by an open circle. These have been averaged using the noise covariance matrix to make the black points. Left: For the Planck best fit cosmology. Right: For the Planck + CFHTLenS $\Lambda$CDM best fit cosmology. Note that because of the extrapolation to the matter power spectrum, both the points and the lines move when the cosmology changes. In the range of the CFHTLenS data points the line moves down by about the same amount as the CFHTLenS points move up, on switching the cosmology from Planck (left panel) to Planck + CFHTLenS (right panel).
• Figure 2: Constraints in the clustering amplitude $\sigma_8$ and dark matter density $\Omega_{\rm{m}}$ plane from Planck+WP and CFHTLenS, assuming our base cosmological model. Filled blue banana: 1 and 2$\sigma$ CFHTLenS only constraints using all $\theta$ bins in $\xi_{+/-}(\theta)$. Dashed green banana: 1 and 2$\sigma$ CFHTLenS only constraints excluding small scales (see Section \ref{['sec:nl']} for cuts on $\theta$). Small, purple contours: The constraints on the base model from Planck+WP. Discrepancy between the 2d marginalised Planck+WP and CFHTLenS contours is clear at the $\sim95\%$ level
• Figure 3: Top panel - the weight functions, $W(log_{10}(k),\theta)$ for $\xi_+(\theta)$, for the autocorrelation of the highest redshift CFHTLenS bin. The weight functions give the relative contribution to $\xi_+(\theta)$ as a function of $k$. The 5 lines are for the 5 $\theta$ bins used (with bin centres at 1.65, 3.58, 7.76, 16.80, 36.18 arcmin), with lower $\theta$ bins peaking at higher $k$. Bottom panel - the nonlinear matter power spectrum at z=0.5 predicted by Coyote and smith03, as a fraction of the takahashi12 prediction.
• Figure 4: CFHTLenS $\sigma_8$ constraints in an otherwise fixed fiducial cosmology, with 3 different nonlinear power spectrum treatments. Also shown is the constraint using takahashi12 and a prescription for AGN feedback described in Section \ref{['sec:bar']}
• Figure 5: 68% and 95% confidence regions in the clustering amplitude $\sigma_8$ and dark matter density $\Omega_{\rm{m}}$ plane from Planck+WP alone and CFHTLenS alone. In all panels, dashed green contours represent the base $\Lambda$CDM constraints from Fig. \ref{['fig:om_s8_base']}. Top left: CFHTLenS with extra IA redshift scaling parameter (filled blue contours) and Planck+WP (smaller purple contours). Top right: CFHTLenS marginalised over an AGN feedback parameter (filled blue contours) and Planck+WP (smaller purple contours). Bottom left: CFHTLenS (blue contours) and Planck+WP (smaller purple contours) allowing varying active neutrino mass. Bottom right: CFHTLenS (blue contours) and Planck+WP (smaller purple contours) allowing a massive sterile neutrino. The black contours are the joint fit.