Weighing the Giants IV: Cosmology and Neutrino Mass

TL;DR

This work integrates robust weak-lensing mass calibration of 50 ROSAT-detected clusters with X-ray follow-up, gas fraction, and multi-wavelength cosmological probes to constrain the cluster mass function and growth of structure. Using a comprehensive likelihood that couples mass observables to a Tinker-based halo mass function within a flat or near-flat cosmology, the authors derive $\Omega_m = 0.26 \pm 0.03$ and $\sigma_8 = 0.83 \pm 0.04$, with $\sigma_8(\Omega_m/0.3)^{0.17} = 0.81 \pm 0.03$, and demonstrate strong consistency with WMAP and Planck CMB results under minimal neutrino mass. They find no compelling evidence for non-zero neutrino mass once lensing-calibrated cluster masses are accounted for, though extended models slightly degrade these limits; the analysis also yields competitive constraints on dark energy parameters, modifications of gravity via the growth index, and primordial non-Gaussianity, highlighting the crucial role of unbiased mass calibration and the potential gains from expanding the redshift reach with future multi-wavelength cluster surveys. The results underscore that accurate cluster-mass calibrations are essential to exploit cluster counts for precision cosmology, including neutrino physics and dark energy, and point to substantial improvements achievable with larger lensing datasets and higher-redshift cluster samples from upcoming surveys.

Abstract

We employ robust weak gravitational lensing measurements to improve cosmological constraints from measurements of the galaxy cluster mass function and its evolution, using X-ray selected clusters detected in the ROSAT All-Sky Survey. Our lensing analysis constrains the absolute mass scale of such clusters at the 8 per cent level, including both statistical and systematic uncertainties. Combining it with the survey data and X-ray follow-up observations, we find a tight constraint on a combination of the mean matter density and late-time normalization of the matter power spectrum, $σ_8(Ω_m/0.3)^{0.17}=0.81\pm0.03$, with marginalized, one-dimensional constraints of $Ω_m=0.26\pm0.03$ and $σ_8=0.83\pm0.04$. For these two parameters, this represents a factor of two improvement in precision with respect to previous work, primarily due to the reduced systematic uncertainty in the absolute mass calibration provided by the lensing analysis. Our new results are in good agreement with constraints from cosmic microwave background (CMB) data, both WMAP and Planck (plus WMAP polarization), under the assumption of a flat $Λ$CDM cosmology with minimal neutrino mass. Consequently, we find no evidence for non-minimal neutrino mass from the combination of cluster data with CMB, supernova and baryon acoustic oscillation measurements, regardless of which all-sky CMB data set is used (and independent of the recent claimed detection of B-modes on degree scales). We also present improved constraints on models of dark energy (both constant and evolving), modifications of gravity, and primordial non-Gaussianity. Assuming flatness, the constraints for a constant dark energy equation of state from the cluster data alone are at the 15 per cent level, improving to $\sim 6$ per cent when the cluster data are combined with other leading probes.

Figures (11)

• Figure 1: Constraints on $\Omega_{\mathrm{m}}$ and $\sigma_8$ from this work (purple shading) and earlier works by these authors (yellow and green shading; Mantz0709.4294, Mantz0909.3098), accounting for systematic uncertainties. Dark and light shading respectively indicate the 68.3 and 95.4 per cent confidence regions. The underlying cluster survey data set is nearly identical across all three generations of results, but the approaches to calibrating cluster masses and the associated scaling relations have incorporated progressively better control of systematic uncertainties, leading to significantly tighter and more robust constraints. Contemporaneous priors on $h$ and $\Omega_{\mathrm{b}} h^2$ are included in each case (the improvement in these priors has negligible effect compared to the mass calibration). These results are essentially identical for flat and non-flat $\Lambda$CDM models, and flat constant-$w$ dark energy models. In evolving-$w$ models and models with the neutrino mass free, the shape of the confidence region changes slightly, but its width ($\sigma_8$ at fixed $\Omega_{\mathrm{m}}$) remains the same.
• Figure 2: Left: Constraints from our cluster data (with standard priors on $h$ and $\Omega_{\mathrm{b}} h^2$) are compared with results from WMAP and Planck+WP CMB data, assuming a flat $\Lambda$CDM cosmology with minimal neutrino mass (assuming the normal mass hierarchy). Dark and light shading respectively indicate the 68.3 and 95.4 per cent confidence regions, including systematic uncertainties. The three sets of constraints are mutually consistent. Right: A number of marginalized constraints on $\sigma_8$ from the literature are compared at a common, concordance value of $\Omega_{\mathrm{m}}=0.3$. Results from clusters are shown by circles (X-ray surveys), squares (optical surveys) or triangles (SZ surveys), with crosses showing CMB constraints. The error bars include each author's estimate of the systematic uncertainties whenever possible (see text for details and references). The shaded, horizontal band reflects the 68.3 per cent confidence interval for our new result (filled circle), $\sigma_8(\Omega_{\mathrm{m}}/0.3)^{0.17}=0.81\pm0.03$. The mass calibration provided by the (blinded) von-der-Linden1208.0597Kelly1208.0602Applegate1208.0605 lensing analysis (reflected by our $\sigma_8$ value) is in agreement with previous work by the same group (Mantz0709.4294; Mantz0909.3098), within the quoted statistical plus systematic uncertainties, and provides good agreement in $\sigma_8$ with CMB measurements, but is offset from some other cluster analyses.
• Figure 3: Left: Marginalized posterior distributions for $\sum m_\nu$, assuming a flat $\Lambda$CDM background and standard value of $N_{\mathrm{eff}}$, from the combination of cluster, CMB, supernova and BAO data. The combined data include either Planck+WP (solid line) or WMAP (dashed line) all-sky CMB data; ACT and SPT CMB data are included in both cases. Vertical, dotted lines indicate the minimum values of $\sum m_\nu$ implied by flavor oscillation measurements for the normal and inverted hierarchies (0.056 and 0.095$\mathrm{\, eV}$, respectively). Both data combinations are consistent with $\sum m_\nu=0$. Right: For the combination using WMAP CMB data (see Appendix \ref{['sec:planckfigs']} for the equivalent Planck+WP figure), we show 68.3 and 95.4 per cent confidence regions on $\sum m_\nu$ and $\sigma_8$ for the flat $\Lambda$CDM+$\sum m_\nu$ ("vanilla") model (yellow/orange shading). The other regions correspond to 95.4 confidence (only) for models with an additional degree of freedom: spatial curvature (blue), the dark energy equation of state (red), the effective number of relativistic species (purple), or the amplitude of primordial tensor perturbations (green). In the latter case, we include the prior $r=0.20^{+0.07}_{-0.05}$, based on measurements by the BICEP2-Collaboration1403.3985. The constraints when not including this additional prior are somewhat tighter (Table \ref{['tab:nu']}).
• Figure 4: Constraints on constant-$w$ dark energy models with minimal neutrino mass from our cluster data (with standard priors on $h$ and $\Omega_{\mathrm{b}} h^2$) are compared with results from CMB (WMAP, ACT and SPT), supernova and BAO (also including priors on $h$ and $\Omega_{\mathrm{b}} h^2$) data, and their combination. The priors on $h$ and $\Omega_{\mathrm{b}} h^2$ are not included in the combined constraints. Dark and light shading respectively indicate the 68.3 and 95.4 per cent confidence regions, accounting for systematic uncertainties.
• Figure 5: Constraints on $\Lambda$CDM models (including curvature) with minimal neutrino mass from our cluster data (with standard priors on $h$ and $\Omega_{\mathrm{b}} h^2$) are compared with results from CMB (WMAP, ACT and SPT), supernova and BAO (also including priors on $h$ and $\Omega_{\mathrm{b}} h^2$) data, and their combination. The priors on $h$ and $\Omega_{\mathrm{b}} h^2$ are not included in the combined constraints. Dark and light shading respectively indicate the 68.3 and 95.4 per cent confidence regions, accounting for systematic uncertainties. The dotted line denotes spatially flat models.