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We present weak-lensing (WL) mass constraints for a sample of massive galaxy clusters detected by the South Pole Telescope (SPT) via the Sunyaev–Zel'dovich effect (SZE). We use griz imaging data obtained from the Science Verification (SV) phase of the Dark Energy Survey (DES) to fit the WL shear signal of 33 clusters in the redshift range 0.25 ≤ |$z$| ≤ 0.8 with NFW profiles and to constrain a four-parameter SPT mass–observable relation. To account for biases in WL masses, we introduce a WL mass to true mass scaling relation described by a mean bias and an intrinsic, lognormal scatter. We allow for correlated scatter within the WL and SZE mass–observable relations and use simulations to constrain priors on nuisance parameters related to bias and scatter from WL. We constrain the normalization of the ζ− M 500 relation, |$A_\mathrm{SZ}=12.0_{-6.7}^{+2.6}$| when using a prior on the mass slope B SZ from the latest SPT cluster cosmology analysis. Without this prior, we recover |$A_\mathrm{SZ}=10.8_{-5.2}^{+2.3}$| and |$B_\mathrm{SZ}=1.30_{-0.44}^{+0.22}$|⁠. Results in both cases imply lower cluster masses than measured in previous work with and without WL, although the uncertainties are large. The WL derived value of B SZ is |${\approx } 20{{\ \rm per\ cent}}$| lower than the value preferred by the most recent SPT cluster cosmology analysis. The method demonstrated in this work is designed to constrain cluster masses and cosmological parameters simultaneously and will form the basis for subsequent studies that employ the full SPT cluster sample together with the DES data. [ABSTRACT FROM AUTHOR]

Recent measurements of the cosmic microwave background (CMB) by the Planck Collaboration have produced arguably the most powerful observational evidence in support of the standard model of cosmology, i.e. the spatially flat ΛCDM paradigm. In this work, we perform model selection tests to examine whether the base CMB temperature and large scale polarization anisotropy data from Planck 2015 (P15; Planck Collaboration XIII) prefer any of eight commonly used one-parameter model extensions with respect to flat ΛCDM. We find a clear preference for models with free curvature, ΩK, or free amplitude of the CMB lensing potential, AL. We also further develop statistical tools to measure tension between data sets. We use a Gaussianization scheme to compute tensions directly from the posterior samples using an entropy-based method, the surprise, as well as a calibrated evidence ratio presented here for the first time. We then proceed to investigate the consistency between the base P15 CMB data and six other CMB and distance data sets. In flat ΛCDM we find a 4.8σ tension between the base P15 CMB data and a distance ladder measurement, whereas the former are consistent with the other data sets. In the curved ΛCDM model we find significant tensions in most of the cases, arising from the well-known low power of the low-l multipoles of the CMB data. In the flat ΛCDM+AL model, however, all data sets are consistent with the base P15 CMB observations except for the CMB lensing measurement, which remains in significant tension. This tension is driven by the increased power of the CMB lensing potential derived from the base P15 CMB constraints in both models, pointing at either potentially unresolved systematic effects or the need for new physics beyond the standard flat ΛCDM model. [ABSTRACT FROM AUTHOR]

This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium. This comparison of X-ray and lensing masses measures the combined bias of X-ray hydrostatic masses from both astrophysical and instrumental sources. While we cannot disentangle the two sources of bias, only the combined bias is relevant for calibrating cosmological measurements using relaxed clusters. Assuming a fixed cosmology, and within a characteristic radius (r2500) determined from the X-ray data, we measure a lensing to X-ray mass ratio of 0.96 ± 9 per cent (stat) ± 9?per cent (sys). We find no significant trends of this ratio with mass, redshift or the morphological indicators used to select the sample. Our results imply that any departures from hydrostatic equilibrium at these radii are offset by calibration errors of comparable magnitude, with large departures of tens-of-percent unlikely. In addition, we find a mean concentration of the sample measured from lensing data of c200=3.0+4.4-1.8. Anticipated short-term improvements in lensing systematics, and a modest expansion of the relaxed lensing sample, can easily increase the measurement precision by 30-50 per cent, leading to similar improvements in cosmological constraints that employ X-ray hydrostatic mass estimates, such as on Ωm from the cluster gas mass fraction. [ABSTRACT FROM AUTHOR]

This is the fourth of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 clusters drawn from the ROSAT All-Sky Survey and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Here we examine the constraints on neutrino properties that are enabled by the precise and robust constraint on the amplitude of the matter power spectrum at low redshift available from our data. In combination with cluster gas mass fraction, cosmic microwave background, supernova and baryon acoustic oscillation data, and incorporating conservative allowances for systematic uncertainties, we limit the species-summed neutrino mass, , to at 95.4 per cent confidence in a spatially flat, cosmological constant (ΛCDM) model. In a flat ΛCDM model where the effective number of neutrino species, Neff, is allowed to vary, we find (68.3 per cent confidence, incorporating a direct constraint on the Hubble parameter from Cepheid and supernova data). We also obtain results with additional degrees of freedom in the cosmological model, in the form of global spatial curvature (Ωk) and a primordial spectrum of tensor perturbations ( r and ). The results are not immune to these generalizations; however, in the most general case we consider, in which , curvature and tensors are all free, we still obtain and (at, respectively, the same confidence levels as above). These results agree well with recent work using independent data and highlight the importance of measuring cosmic structure and expansion at low as well as high redshifts. Although our cluster data extend to redshift , the direct effect of neutrino mass on the growth of structure at late times is not yet detected at a significant level. [ABSTRACT FROM AUTHOR]

This is the second in a series of papers in which we derive simultaneous constraints on cosmology and X-ray scaling relations using observations of massive, X-ray flux-selected galaxy clusters. The data set consists of 238 clusters with 0.1–2.4 keV luminosities , and incorporates follow-up observations of 94 of those clusters using the Chandra X-ray Observatory or ROSAT (11 were observed with both). The clusters are drawn from three samples based on the ROSAT All-Sky Survey: the ROSAT Brightest Cluster Sample (78/37 clusters detected/followed-up), the ROSAT-ESO Flux-Limited X-ray sample (126/25) and the bright sub-sample of the Massive Cluster Survey (34/32). Our analysis accounts self-consistently for all selection effects, covariances and systematic uncertainties. Here we describe the reduction of the follow-up X-ray observations, present results on the cluster scaling relations, and discuss their implications. Our constraints on the luminosity–mass and temperature–mass relations, measured within r500, lead to three important results. First, the data support the conclusion that excess heating of the intracluster medium (or a combination of heating and condensation of the coldest gas) has altered its thermodynamic state from that expected in a simple, gravitationally dominated system; however, this excess heat is primarily limited to the central regions of clusters . Secondly, the intrinsic scatter in the centre-excised luminosity–mass relation is remarkably small, being bounded at the <10 per cent level in current data; for the hot, massive clusters under investigation, this scatter is smaller than in either the temperature–mass or –mass relations (10–15 per cent). Thirdly, the evolution with redshift of the scaling relations is consistent with the predictions of simple, self-similar models of gravitational collapse, indicating that the mechanism responsible for heating the central regions of clusters was in operation before redshift 0.5 (the limit of our data) and that its effects on global cluster properties have not evolved strongly since then. Our results provide a new benchmark for comparison with numerical simulations of cluster formation and evolution. [ABSTRACT FROM AUTHOR]

This is the first of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 cluster detections from the ROSAT All-Sky Survey, and incorporates follow-up observations of 94 of those clusters using the Chandra X-ray Observatory or ROSAT. Here we describe and implement a new statistical framework required to self-consistently produce simultaneous constraints on cosmology and scaling relations from such data, and present results on models of dark energy. In spatially flat models with a constant dark energy equation of state, w, the cluster data yield and , incorporating standard priors on the Hubble parameter and mean baryon density of the Universe, and marginalizing over conservative allowances for systematic uncertainties. These constraints agree well and are competitive with independent data in the form of cosmic microwave background anisotropies, type Ia supernovae, cluster gas mass fractions, baryon acoustic oscillations, galaxy redshift surveys and cosmic shear. The combination of our data with current microwave background, supernova, gas mass fraction and baryon acoustic oscillation data yields and for flat, constant w models. The combined data also allow us to investigate evolving w models. Marginalizing over transition redshifts in the range 0.05–1, we constrain the equation of state at late and early times to be respectively and , again including conservative systematic allowances. The combined data provide constraints equivalent to a Dark Energy Task Force figure of merit of 15.5. Our results highlight the power of X-ray studies, which enable the straightforward production of large, complete and pure cluster samples and admit tight scaling relations, to constrain cosmology. However, the new statistical framework we apply to this task is equally applicable to cluster studies at other wavelengths. [ABSTRACT FROM AUTHOR]

We present constraints on the mean matter density, Ωm, the normalization of the density fluctuation power spectrum, σ8, and the dark energy equation of state parameter, w, obtained from measurements of the X-ray luminosity function of the largest known galaxy clusters at redshifts z < 0.7, as compiled in the Massive Cluster Survey (MACS) and the local Brightest Cluster Sample (BCS) and ROSAT–ESO Flux Limited X-Ray (REFLEX) galaxy cluster sample. Our analysis employs an observed mass–luminosity relation, calibrated by hydrodynamical simulations, including corrections for non-thermal pressure support and accounting for the presence of intrinsic scatter. Conservative allowances for all known systematic uncertainties are included, as are standard priors on the Hubble constant and mean baryon density. We find and for a spatially flat, cosmological constant model, and and for a flat, constant w model (marginalized 68 per cent confidence intervals). Our findings constitute the first determination of the dark energy equation of state from measurements of the growth of cosmic structure in galaxy clusters, and the consistency of our result with w=−1 lends additional support to the cosmological constant model. Future work improving our understanding of redshift evolution and observational biases affecting the mass–X-ray luminosity relation have the potential to significantly tighten these constraints. Our results are consistent with those from recent analyses of Type Ia supernovae, cosmic microwave background anisotropies, the X-ray gas mass fraction of relaxed galaxy clusters, baryon acoustic oscillations and cosmic shear. Combining the new X-ray luminosity function data with current supernova, cosmic microwave background and cluster gas fraction data yields the improved constraints and . [ABSTRACT FROM AUTHOR]

We present constraints on the mean matter density, Ωm, dark energy density, ΩDE, and the dark energy equation of state parameter, w, using Chandra measurements of the X-ray gas mass fraction ( fgas) in 42 hot ( kT > 5 keV), X-ray luminous, dynamically relaxed galaxy clusters spanning the redshift range 0.05 < z < 1.1. Using only the fgas data for the six lowest redshift clusters at z < 0.15, for which dark energy has a negligible effect on the measurements, we measure (68 per cent confidence limits, using standard priors on the Hubble constant, H0, and mean baryon density, ). Analysing the data for all 42 clusters, employing only weak priors on H0 and , we obtain a similar result on Ωm and a detection of the effects of dark energy on the distances to the clusters at ∼99.99 per cent confidence, with for a non-flat ΛCDM model. The detection of dark energy is comparable in significance to recent type Ia supernovae (SNIa) studies and represents strong, independent evidence for cosmic acceleration. Systematic scatter remains undetected in the fgas data, despite a weighted mean statistical scatter in the distance measurements of only ∼5 per cent. For a flat cosmology with a constant dark energy equation of state, we measure and w=−1.14 ± 0.31. Combining the fgas data with independent constraints from cosmic microwave background and SNIa studies removes the need for priors on and H0 and leads to tighter constraints: and w=−0.98 ± 0.07 for the same constant- w model. Our most general analysis allows the equation of state to evolve with redshift. Marginalizing over possible transition redshifts 0.05 < zt < 1, the combined fgas+ CMB + SNIa data set constrains the dark energy equation of state at late and early times to be and , respectively, in agreement with the cosmological constant paradigm. Relaxing the assumption of flatness weakens the constraints on the equation of state by only a factor of ∼2. Our analysis includes conservative allowances for systematic uncertainties associated with instrument calibration, cluster physics and data modelling. The measured small systematic scatter, tight constraint on Ωm and powerful constraints on dark energy from the fgas data bode well for future dark energy studies using the next generation of powerful X-ray observatories, such as Constellation-X. [ABSTRACT FROM AUTHOR]