Canada-France-Hawaii Telescope Lensing Survey Research Articles

Detecting Anomalous Images in Astronomical Datasets

Environmental and instrumental conditions can cause anomalies in astronomical images, which can potentially bias all kinds of measurements if not excluded. Detection of the anomalous images is usually done by human eyes, which is slow and sometimes not accurate. This is an important issue in weak lensing studies, particularly in the era of large-scale galaxy surveys, in which image qualities are crucial for the success of galaxy shape measurements. In this work we present two automatic methods for detecting anomalous images in astronomical data sets. The anomalous features can be divided into two types: one is associated with the source images, and the other appears on the background. Our first method, called the entropy method, utilizes the randomness of the orientation distribution of the source shapes and the background gradients to quantify the likelihood of an exposure being anomalous. Our second method involves training a neural network (autoencoder) to detect anomalies. We evaluate the effectiveness of the entropy method on the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS) and Dark Energy Camera Legacy Survey (DECaLS DR3) data. In CFHTLenS, with 1171 exposures, the entropy method outperforms human inspection by detecting 12 of the 13 anomalous exposures found during human inspection and uncovering 10 new ones. In DECaLS DR3, with 17112 exposures, the entropy method detects a significant number of anomalous exposures while keeping a low false-positive rate. We find that although the neural network performs relatively well in detecting source anomalies, its current performance is not as good as the entropy method.

Data-driven templates with dictionary learning and sparse representations for photometric redshift estimation

The quality of photometric redshift estimates is fundamental for cosmological applications, as the constraints on the cosmological parameters obtained by the photometric surveys strongly rely on their precision and accuracy. In order to obtain reliable redshift estimates, a large number of studies have proposed different algorithms based on SED template fitting and machine learning methodologies. While template fitting strategies do not need spectroscopic data for training, they also provide consistent estimates in most scenarios. On the other hand, machine learning-based approaches succeed at building a mapping function between the input space (composed by magnitudes and other physical parameters) and the target photometric redshift space. These empirical methods lead to more accurate results as long as the spectroscopic ground truth properly represents the actual galaxy population distribution. Thus, combining template fitting and machine learning techniques would allow to leverage the advantages of both methodologies yielding hybrid methods. The goal is to provide a good estimation accuracy while maximizing the photometric range coverage. This is particularly important in the high-z regime, where the spectroscopic training sample is rarely available. We propose in this article a new method to derive data-driven templates from simulated spectra using dictionary learning. As these representations are obtained directly from the data, they allow to capture the physical properties of the galaxies better than theoretical templates. Inspired by hybrid algorithms, the dictionary is built hierarchically and the features of the different types of galaxies are separated. Once the dictionary has been created, the data-driven templates are artificially redshifted and the observed spectra are sparsely decomposed on this dictionary. The value providing the minimum reconstruction error is selected as the photometric redshift estimate. This new technique, astride template fitting and machine learning, builds representations for the galaxy spectra through unsupervised learning and computes the photometric redshifts by χ2 minimization. The performance of the algorithm has been evaluated on realistic galaxy photometric simulations as well as on real data from the Canada–France–Hawaii Telescope Lensing Survey.

CFHTLenS: Galaxy bias as function of scale, stellar mass, and colour

Galaxy models predict a tight relation between the clustering of galaxies and dark matter on cosmological scales, but predictions differ notably in the details. We used this opportunity and tested two semi-analytic models by the Munich and Durham groups with data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). For the test we measured the scale-dependent galaxy bias factor b(k) and correlation factor r(k) from linear to non-linear scales of k ≈ 10 h Mpc−1 at two redshifts z̄ = 0.35, 0.51 for galaxies with stellar mass between 5 × 109 and 3 × 1011 h70−2 M⊙. Our improved gravitational lensing technique accounts for the intrinsic alignment of sources and the magnification of lens galaxies for better constraints for the galaxy-matter correlation r(k). Galaxy bias in CFHTLenS increases with k and stellar mass; it is colour-dependent, revealing the individual footprints of galaxy types. Despite a reasonable model agreement for the relative change with both scale and galaxy properties, there is a clear conflict for b(k) with no model preference: the model galaxies are too weakly clustered. This may flag a model problem at z ≳ 0.3 for all stellar masses. As in the models, however, there is a high correlation r(k) between matter and galaxy density on all scales, and galaxy bias is typically consistent with a deterministic bias on linear scales. Only our blue and low-mass galaxies of about 7 × 109 h70−2 M⊙ at z̄ = 0.51 show, contrary to the models, a weak tendency towards a stochastic bias on linear scales where rls = 0.75 ± 0.14 (stat.) ± 0.06 (sys.). This result is of interest for cosmological probes, such as EG, that rely on a deterministic galaxy bias. We provide Monte Carlo realisations of posterior constraints for b(k) and r(k) in CFHTLenS for every galaxy sample in this paper at the CDS.

The matter fluctuation amplitude inferred from the weak lensing power spectrum and correlation function in CFHTLenS data

ABSTRACT Based on the cosmic shear data from the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS), Kilbinger et al. obtained a constraint on the amplitude of matter fluctuations of σ8(Ωm/0.27)0.6 = 0.79 ± 0.03 from the two-point correlation function (2PCF). This is ≈3σ lower than the value 0.89 ± 0.01 derived from Planck data on cosmic microwave background (CMB) anisotropies. On the other hand, based on the same CFHTLenS data, but using the power spectrum, and performing a different analysis, Liu et al. obtained the higher value of $\sigma _8(\Omega _\mathrm{m}/0.27)^{0.64}=0.87^{+0.05}_{-0.06}$. We here investigate the origin of this difference, by performing a fair side-by-side comparison of the 2PCF and power spectrum analyses on CFHTLenS data. We find that these two statistics indeed deliver different results, even when applied to the same data in an otherwise identical procedure. We identify excess power in the data on small scales (ℓ > 5000) driving the larger values inferred from the power spectrum. We speculate on the possible origin of this excess small-scale power. More generally, our results highlight the utility of analysing the 2PCF and the power spectrum in tandem, to discover (and to help control) systematic errors.

Galaxy shape measurement with convolutional neural networks

ABSTRACT We present our results from training and evaluating a convolutional neural network (CNN) to predict galaxy shapes from wide-field survey images of the first data release of the Dark Energy Survey (DES DR1). We use conventional shape measurements as ‘ground truth’ from an overlapping, deeper survey with less sky coverage, the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS). We demonstrate that CNN predictions from single band DES images reproduce the results of CFHTLenS at bright magnitudes and show higher correlation with CFHTLenS at fainter magnitudes than maximum likelihood model fitting estimates in the DES Y1 im3shape catalogue. Prediction of shape parameters with a CNN is also extremely fast, it takes only 0.2 ms per galaxy, improving more than 4 orders of magnitudes over forward model fitting. The CNN can also accurately predict shapes when using multiple images of the same galaxy, even in different colour bands, with no additional computational overhead. The CNN is again more precise for faint objects, and the advantage of the CNN is more pronounced for blue galaxies than red ones when compared to the DES Y1 metacalibration catalogue, which fits a single Gaussian profile using riz band images. We demonstrate that CNN shape predictions within the metacalibration self-calibrating framework yield shear estimates with negligible multiplicative bias, m < 10−3, and no significant point spread function (PSF) leakage. Our proposed set-up is applicable to current and next-generation weak lensing surveys where higher quality ‘ground truth’ shapes can be measured in dedicated deep fields.

Consistent cosmic shear in the face of systematics: a B-mode analysis of KiDS-450, DES-SV and CFHTLenS

We analyse three public cosmic shear surveys; the Kilo-Degree Survey (KiDS-450), the Dark Energy Survey (DES-SV) and the Canada France Hawaii Telescope Lensing Survey (CFHTLenS). Adopting the “COSEBIs” statistic to cleanly and completely separate the lensing E-modes from the non-lensing B-modes, we detect B-modes in KiDS-450 and CFHTLenS at the level of ∼2.7σ. For DES-SV we detect B-modes at the level of 2.8σ in a non-tomographic analysis, increasing to a 5.5σB-mode detection in a tomographic analysis. In order to understand the origin of these detected B-modes we measure the B-mode signature of a range of different simulated systematics including PSF leakage, random but correlated PSF modelling errors, camera-based additive shear bias and photometric redshift selection bias. We show that any correlation between photometric-noise and the relative orientation of the galaxy to the point-spread-function leads to an ellipticity selection bias in tomographic analyses. This work therefore introduces a new systematic for future lensing surveys to consider. We find that the B-modes in DES-SV appear similar to a superposition of the B-mode signatures from all of the systematics simulated. The KiDS-450 and CFHTLenS B-mode measurements show features that are consistent with a repeating additive shear bias.

Comparison of the excess mass around CFHTLenS galaxy-pairs to predictions from a semi-analytic model using galaxy-galaxy-galaxy lensing

The matter environment of galaxies is connected to the physics of galaxy formation and evolution. In particular, the average matter distribution around galaxy pairs is a strong test for galaxy models. Utilising galaxy-galaxy-galaxy lensing as a direct probe, we map out the distribution of correlated surface mass-density around galaxy pairs in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We have compared, for the first time, these so-called excess mass maps to predictions provided by a recent semi-analytic model, which is implanted within the dark-matter Millennium Simulation. We analysed galaxies with stellar masses between 109 − 1011 M⊙ in two photometric redshift bins, for lens redshifts z ≲ 0.6. The projected separation of the galaxy pairs ranges between 170 − 300 h−1 kpc, thereby focusing on pairs inside groups and clusters. To allow us a better interpretation of the maps, we discuss the impact of chance pairs, that is galaxy pairs that appear close to each other in projection only. We have introduced an alternative correlation map that is less affected by projection effects but has a lower signal-to-noise ratio. Our tests with synthetic data demonstrate that the patterns observed in both types of maps are essentially produced by correlated pairs which are close in redshift (Δz ≲ 5 × 10−3). We also verify the excellent accuracy of the map estimators. In an application to the galaxy samples in the CFHTLenS, we obtain a 3σ − 6σ significant detection of the excess mass and an overall good agreement with the galaxy model predictions. There are, however, a few localised spots in the maps where the observational data disagrees with the model predictions on a ≈3.5σ confidence level. Although we have no strong indications for systematic errors in the maps, this disagreement may be related to the residual B-mode pattern observed in the average of all maps. Alternatively, misaligned galaxy pairs inside dark matter halos or lensing by a misaligned distribution of the intra-cluster gas might also cause the unanticipated bulge in the distribution of the excess mass between lens pairs.

A unified analysis of four cosmic shear surveys

In the past few years, several independent collaborations have presented cosmological constraints from tomographic cosmic shear analyses. These analyses differ in many aspects: the datasets, the shear and photometric redshift estimation algorithms, the theory model assumptions, and the inference pipelines. To assess the robustness of the existing cosmic shear results, we present in this paper a unified analysis of four of the recent cosmic shear surveys: the Deep Lens Survey (DLS), the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), the Science Verification data from the Dark Energy Survey (DES-SV), and the 450 deg$^{2}$ release of the Kilo-Degree Survey (KiDS-450). By using a unified pipeline, we show how the cosmological constraints are sensitive to the various details of the pipeline. We identify several analysis choices that can shift the cosmological constraints by a significant fraction of the uncertainties. For our fiducial analysis choice, considering a Gaussian covariance, conservative scale cuts, assuming no baryonic feedback contamination, identical cosmological parameter priors and intrinsic alignment treatments, we find the constraints (mean, 16% and 84% confidence intervals) on the parameter $S_{8}\equiv \sigma_{8}(\Omega_{\rm m}/0.3)^{0.5}$ to be $S_{8}=0.94_{-0.045}^{+0.046}$ (DLS), $0.66_{-0.071}^{+0.070}$ (CFHTLenS), $0.84_{-0.061}^{+0.062}$ (DES-SV) and $0.76_{-0.049}^{+0.048}$ (KiDS-450). From the goodness-of-fit and the Bayesian evidence ratio, we determine that amongst the four surveys, the two more recent surveys, DES-SV and KiDS-450, have acceptable goodness-of-fit and are consistent with each other. The combined constraints are $S_{8}=0.79^{+0.042}_{-0.041}$, which is in good agreement with the first year of DES cosmic shear results and recent CMB constraints from the Planck satellite.

Precision calculations of the cosmic shear power spectrum projection

We compute the spherical-sky weak-lensing power spectrum of the shear and convergence. We discuss various approximations, such as flat-sky, and first- and second- order Limber equations for the projection. We find that the impact of adopting these approximations is negligible when constraining cosmological parameters from current weak lensing surveys. This is demonstrated using data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We find that the reported tension with Planck Cosmic Microwave Background (CMB) temperature anisotropy results cannot be alleviated. For future large-scale surveys with unprecedented precision, we show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for l > 3, with the corresponding errors an order of magnitude below cosmic variance for all l. When computing the two-point shear correlation function, we show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, our numerical implementation of all approximations and the full projection are publicly available within the package nicaea at http://www.cosmostat.org/software/nicaea.

Confronting semi-analytic galaxy models with galaxy-matter correlations observed by CFHTLenS

Testing predictions of semi-analytic models of galaxy evolution against observations help to understand the complex processes that shape galaxies. We compare predictions from the Garching and Durham models implemented on the Millennium Run with observations of galaxy-galaxy lensing (GGL) and galaxy-galaxy-galaxy lensing (G3L) for various galaxy samples with stellar masses in the range 0.5 < (M_* / 10^10 M_Sun) < 32 and photometric redshift range 0.2 < z < 0.6 in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We find that the predicted GGL and G3L signals are in qualitative agreement with CFHTLenS data. Quantitatively, the models succeed in reproducing the observed signals in the highest stellar mass bin (16 < ( M_* / 10^10 M_Sun) < 32) but show different degrees of tension for the other stellar mass samples. The Durham models are strongly excluded at the 95% confidence level by the observations as they largely over-predict the amplitudes of the GGL and G3L signals, probably because they predict too many satellite galaxies in massive halos.

Cross-correlation of weak lensing and gamma rays: implications for the nature of dark matter

We measure the cross-correlation between Fermi-LAT gamma-ray photons and over 1000 deg$^2$ of weak lensing data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), the Red Cluster Sequence Lensing Survey (RCSLenS), and the Kilo Degree Survey (KiDS). We present the first measurement of tomographic weak lensing cross-correlations and the first application of spectral binning to cross-correlations between gamma rays and weak lensing. The measurements are performed using an angular power spectrum estimator while the covariance is estimated using an analytical prescription. We verify the accuracy of our covariance estimate by comparing it to two internal covariance estimators. Based on the non-detection of a cross-correlation signal, we derive constraints on weakly interacting massive particle (WIMP) dark matter. We compute exclusion limits on the dark matter annihilation cross-section $\langle\sigma_\rm{ann} v \rangle$, decay rate $\Gamma_\rm{dec}$, and particle mass $m_\rm{DM}$. We find that in the absence of a cross-correlation signal, tomography does not significantly improve the constraining power of the analysis. Assuming a strong contribution to the gamma-ray flux due to small-scale clustering of dark matter and accounting for known astrophysical sources of gamma rays, we exclude the thermal relic cross-section for particle masses of $m_\rm{DM}\lesssim 20$ GeV.

Systematic tests for position-dependent additive shear bias

We present new tests to identify stationary position-dependent additive shear biases in weak gravitational lensing data sets. These tests are important diagnostics for currently ongoing and planned cosmic shear surveys, as such biases induce coherent shear patterns that can mimic and potentially bias the cosmic shear signal. The central idea of these tests is to determine the average ellipticity of all galaxies with shape measurements in a grid in the pixel plane. The distribution of the absolute values of these averaged ellipticities can be compared to randomized catalogues; a difference points to systematics in the data. In addition, we introduce a method to quantify the spatial correlation of the additive bias, which suppresses the contribution from cosmic shear and therefore eases the identification of a position-dependent additive shear bias in the data. We apply these tests to the publicly available shear catalogues from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) and the Kilo Degree Survey (KiDS) and find evidence for a small but non-negligible residual additive bias at small scales. As this residual bias is smaller than the error on the shear correlation signal at those scales, it is highly unlikely that it causes a significant bias in the published cosmic shear results of CFHTLenS. In CFHTLenS, the amplitude of this systematic signal is consistent with zero in fields where the number of stars used to model the PSF is higher than average, suggesting that the position-dependent additive shear bias originates from undersampled PSF variations across the image.

CFHTLenS revisited: assessing concordance with Planck including astrophysical systematics

We investigate the impact of astrophysical systematics on cosmic shear cosmological parameter constraints from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), and the concordance with cosmic microwave background measurements by Planck. We present updated CFHTLenS cosmic shear tomography measurements extended to degree scales using a covariance calibrated by a new suite of N-body simulations. We analyze these measurements with a new model fitting pipeline, accounting for key systematic uncertainties arising from intrinsic galaxy alignments, baryonic effects in the nonlinear matter power spectrum, and photometric redshift uncertainties. We examine the impact of the systematic degrees of freedom on the cosmological parameter constraints, both independently and jointly. When the systematic uncertainties are considered independently, the intrinsic alignment amplitude is the only degree of freedom that is substantially preferred by the data. When the systematic uncertainties are considered jointly, there is no consistently strong preference in favor of the more complex models. We quantify the level of concordance between the CFHTLenS and Planck datasets by employing two distinct data concordance tests, grounded in Bayesian evidence and information theory. We find that the two data concordance tests largely agree with one another, and that the level of concordance between the CFHTLenS and Planck datasets is sensitive to the exact details of the systematic uncertainties included in our analysis, ranging from decisive discordance to substantial concordance as the treatment of the systematic uncertainties becomes more conservative. The least conservative scenario is the one most favored by the cosmic shear data, but it is also the one that shows the greatest degree of discordance with Planck. The data and analysis code are public at https://github.com/sjoudaki/cfhtlens_revisited

Star–galaxy classification using deep convolutional neural networks

Most existing star-galaxy classifiers use the reduced summary information from catalogs, requiring careful feature extraction and selection. The latest advances in machine learning that use deep convolutional neural networks allow a machine to automatically learn the features directly from data, minimizing the need for input from human experts. We present a star-galaxy classification framework that uses deep convolutional neural networks (ConvNets) directly on the reduced, calibrated pixel values. Using data from the Sloan Digital Sky Survey (SDSS) and the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), we demonstrate that ConvNets are able to produce accurate and well-calibrated probabilistic classifications that are competitive with conventional machine learning techniques. Future advances in deep learning may bring more success with current and forthcoming photometric surveys, such as the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST), because deep neural networks require very little, manual feature engineering.

CFHTLenS and RCSLenS: testing photometric redshift distributions using angular cross-correlations with spectroscopic galaxy surveys

We determine the accuracy of galaxy redshift distributions as estimated from photometric redshift probability distributions $p(z)$. Our method utilises measurements of the angular cross-correlation between photometric galaxies and an overlapping sample of galaxies with spectroscopic redshifts. We describe the redshift leakage from a galaxy photometric redshift bin $j$ into a spectroscopic redshift bin $i$ using the sum of the $p(z)$ for the galaxies residing in bin $j$. We can then predict the angular cross-correlation between photometric and spectroscopic galaxies due to intrinsic galaxy clustering when $i \neq j$ as a function of the measured angular cross-correlation when $i=j$. We also account for enhanced clustering arising from lensing magnification using a halo model. The comparison of this prediction with the measured signal provides a consistency check on the validity of using the summed $p(z)$ to determine galaxy redshift distributions in cosmological analyses, as advocated by the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We present an analysis of the photometric redshifts measured by CFHTLenS, which overlaps the Baryon Oscillation Spectroscopic Survey (BOSS). We also analyse the Red-sequence Cluster Lensing Survey (RCSLenS), which overlaps both BOSS and the WiggleZ Dark Energy Survey. We find that the summed $p(z)$ from both surveys are generally biased with respect to the true underlying distributions. If unaccounted for, this bias would lead to errors in cosmological parameter estimation from CFHTLenS by less than $\sim 4\%$. For photometric redshift bins which spatially overlap in 3-D with our spectroscopic sample, we determine redshift bias corrections which can be used in future cosmological analyses that rely on accurate galaxy redshift distributions.

RCSLenS: The Red Cluster Sequence Lensing Survey

We present the Red-sequence Cluster Lensing Survey (RCSLenS), an application of the methods developed for the Canada France Hawaii Telescope Lensing Survey (CFHTLenS) to the ~785deg$^2$, multi-band imaging data of the Red-sequence Cluster Survey 2 (RCS2). This project represents the largest public, sub-arcsecond seeing, multi-band survey to date that is suited for weak gravitational lensing measurements. With a careful assessment of systematic errors in shape measurements and photometric redshifts we extend the use of this data set to allow cross-correlation analyses between weak lensing observables and other data sets. We describe the imaging data, the data reduction, masking, multi-colour photometry, photometric redshifts, shape measurements, tests for systematic errors, and a blinding scheme to allow for more objective measurements. In total we analyse 761 pointings with r-band coverage, which constitutes our lensing sample. Residual large-scale B-mode systematics prevent the use of this shear catalogue for cosmic shear science. The effective number density of lensing sources over an unmasked area of 571.7deg$^2$ and down to a magnitude limit of r~24.5 is 8.1 galaxies per arcmin$^2$ (weighted: 5.5 arcmin$^{-2}$) distributed over 14 patches on the sky. Photometric redshifts based on 4-band griz data are available for 513 pointings covering an unmasked area of 383.5 deg$^2$ We present weak lensing mass reconstructions of some example clusters as well as the full survey representing the largest areas that have been mapped in this way. All our data products are publicly available through CADC at http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/community/rcslens/query.html in a format very similar to the CFHTLenS data release.

A pseudo-spectrum analysis of galaxy–galaxy lensing

We present the application of the pseudo-spectrum method to galaxy-galaxy lensing. We derive explicit expressions for the pseudo-spectrum analysis of the galaxy-shear cross spectrum, which is the Fourier space counterpart of the stacked galaxy-galaxy lensing profile. The pseudo-spectrum method corrects observational issues such as the survey geometry, masks of bright stars and their spikes, and inhomogeneous noise, which distort the spectrum and also mix the E-mode and the B-mode signals. Using ray-tracing simulations in N-body simulations including realistic masks, we confirm that the pseudo-spectrum method successfully recovers the input galaxy-shear cross spectrum. We also investigate the covariance of the galaxy-shear cross spectrum using the ray-tracing simulations to show that there is an excess covariance relative to the Gaussian covariance at small scales where the shot noise is dominated in the Gaussian approximation. We find that the excess of the covariance is consistent with the expectation from the halo sample variance (HSV), which originates from the matter fluctuations at scales larger than the survey area. We apply the pseudo-spectrum method to the observational data of Canada-France-Hawaii Telescope Lensing survey (CFHTLenS) shear catalogue and three different spectroscopic samples of Sloan Digital Sky Survey Luminous Red Galaxy (SDSS LRG), and Baryon Oscillation Spectroscopic Survey (BOSS) CMASS and LOWZ galaxies. The galaxy-shear cross spectra are significantly detected at the level of 7-10$\sigma$ using the analytic covariance with the HSV contribution included. We also confirm that the observed spectra are consistent with the halo model predictions with the halo occupation distribution parameters estimated from previous work. This work demonstrates the viability of galaxy-galaxy lensing analysis in the Fourier space.

Constraining multiplicative bias in CFHTLenS weak lensing shear data

Several recent cosmological analyses have found tension between constraints derived from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) data and those derived from other data sets, such as the Planck cosmic microwave background (CMB) temperature anisotropies. Similarly, a direct cross-correlation of the CFHTLenS data with Planck CMB lensing data yielded an anomalously low amplitude compared to expectations based on Planck or WMAP-derived cosmological parameters (Liu & Hill 2015). One potential explanation for these results is a multiplicative bias afflicting the CFHTLenS galaxy shape measurements, from which shears are inferred. Simulations are used in the CFHTLenS pipeline to calibrate such biases, but no data-driven constraints have been presented to date. In this paper, we cross-correlate CFHTLenS galaxy density maps with CFHTLenS shear maps and Planck CMB lensing maps to calibrate an additional multiplicative shear bias (m) in CFHTLenS (beyond the multiplicative correction that has already been applied to the CFHTLenS galaxy shears), following methods suggested by Vallinotto (2012) and Das et al. (2013). We analyze three magnitude-limited galaxy samples, finding 2-4sigma evidence for m<1 using the deepest sample (i<24), while the others are consistent with m=1 (no bias). This matches the expectation that the shapes of faint galaxies are the most prone to measurement biases. Our results for m are essentially independent of the assumed cosmology, and only weakly sensitive to assumptions about the galaxy bias. We consider three galaxy bias models, finding in all cases that the best-fit multiplicative shear bias is less than unity. A value of m~0.9 would suffice to reconcile the amplitude of density fluctuations inferred from the CFHTLenS shear two-point statistics with that inferred from Planck CMB temperature data. This scenario is consistent with our results.

Testing Hu–Sawickif(R) gravity with the effective field theory approach

We show how to fully map a specific model of modified gravity into the Einstein–Boltzmann solver eftcamb. This approach consists in few steps and allows to obtain the cosmological phenomenology of a model with minimal effort. We discuss all these steps, from the solution of the dynamical equations for the cosmological background of the model to the use of the mapping relations to cast the model into the effective field theory language and use the latter to solve for perturbations. We choose the Hu–Sawicki f(R) model of gravity as our working example. After solving the background and performing the mapping, we interface the algorithm with eftcamb and take advantage of the effective field theory framework to integrate the full dynamics of linear perturbations, returning all quantities needed to accurately compare the model with observations. We discuss some observational signatures of this model, focusing on the linear growth of cosmic structures. In particular we present the behaviour of fσ8 and EG that, unlike the Λ cold dark matter (ΛCDM) scenario, are generally scale dependent in addition to redshift dependent. Finally, we study the observational implications of the model by comparing its cosmological predictions to the Planck 2015 data, including cosmic microwave background lensing, the WiggleZ galaxy survey and the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS), weak-lensing survey measurements. We find that while WiggleZ data favour a non-vanishing value of the Hu–Sawicki model parameter, |$\log _{10}(-f^0_{R})$|⁠, and consequently a large value of σ8, CFHTLenS drags the estimate of |$\log _{10}(-f^0_{R})$| back to the ΛCDM limit.

RCSLenS: testing gravitational physics through the cross-correlation of weak lensing and large-scale structure

The unknown nature of dark energy motivates continued cosmological tests of large-scale gravitational physics. We present a new consistency check based on the relative amplitude of non-relativistic galaxy peculiar motions, measured via redshift-space distortion, and the relativistic deflection of light by those same galaxies traced by galaxy-galaxy lensing. We take advantage of the latest generation of deep, overlapping imaging and spectroscopic datasets, combining the Red Cluster Sequence Lensing Survey (RCSLenS), the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), the WiggleZ Dark Energy Survey and the Baryon Oscillation Spectroscopic Survey (BOSS). We quantify the results using the "gravitational slip" statistic E_G, which we estimate as 0.48 +/- 0.10 at z=0.32 and 0.30 +/- 0.07 at z=0.57, the latter constituting the highest redshift at which this quantity has been determined. These measurements are consistent with the predictions of General Relativity, for a perturbed Friedmann-Robertson-Walker metric in a Universe dominated by a cosmological constant, which are E_G = 0.41 and 0.36 at these respective redshifts. The combination of redshift-space distortion and gravitational lensing data from current and future galaxy surveys will offer increasingly stringent tests of fundamental cosmology.