CFHTLenS: A Gaussian likelihood is a sufficient approximation for a cosmological analysis of third-order cosmic shear statistics
P. Simon, E. Semboloni, L. van Waerbeke, H. Hoekstra, T. Erben, L. Fu, J. Harnois-Déraps, C. Heymans, H. Hildebrandt, M. Kilbinger, T. D. Kitching, L. Miller, T. Schrabback
备注：
21 pages, 13 figures, accepted by MNRAS; edit of arXiv abstract; files are unchanged
We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopted a non-Gaussian model of the data likelihood which is supported by our simulations of the survey. We find that for state-of-the-art surveys, similar to CFHTLenS, a Gaussian likelihood analysis is a reasonable approximation, albeit small differences in the parameter constraints are already visible. For future surveys we expect that a Gaussian model becomes inaccurate. Our algorithm for a refined non-Gaussian analysis and data compression is then of great utility especially because it is not much more elaborate if simulated data are available. Applying this algorithm to the third-order correlations of shear alone in a blind analysis, we find a good agreement with the standard cosmological model: $Σ_8$=$σ_8$ $(Ω_{\rm m}/0.27)^{0.64}$=$0.79^{+0.08}_{-0.11}$ for a flat $Λ\rm CDM$ cosmology with $h=0.7\pm0.04$ ($68\%$ credible interval). Nevertheless our models provide only moderately good fits as indicated by $χ^2/{\rm dof}=2.9$, including a $20\%$ r.m.s. uncertainty in the predicted signal amplitude. The models cannot explain a signal drop on scales around 15 arcmin, which may be caused by systematics. It is unclear whether the discrepancy can be fully explained by residual PSF systematics of which we find evidence at least on scales of a few arcmin. Therefore we need a better understanding of higher-order correlations of cosmic shear and their systematics to confidently apply them as cosmological probes.
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 s…
We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the CFHTLenS weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on …
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 about 2.7 $σ$. For DES- SV we detect B-modes at the level of 2.8 $σ$ in a non-tomographic analysis, increasing to a 5.5 $σ$ B-mode detection in a tomographic analysis. In order to understand the origin of these detected B-modes we measure the B-m…
We present a re-analysis of the CFHTLenS weak gravitational lensing survey using Complete Orthogonal Sets of E/B-mode Integrals, known as COSEBIs. COSEBIs provide a complete set of functions to efficiently separate E-modes from B-modes and hence allow for robust and stringent tests for systematic errors in the data. This analysis reveals significant B-modes on large angular scales that were not previously seen using the standard E/B decomposition analyses. We find that the significance of the B-modes is enhanced when the data is split by galaxy type and analysed in tomographic redshift bins. A…
We present the cluster mass-richness scaling relation calibrated by a weak lensing analysis of >18000 galaxy cluster candidates in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). Detected using the 3D-Matched-Filter cluster-finder of Milkeraitis et al., these cluster candidates span a wide range of masses, from the small group scale up to $\sim10^{15} M_{\odot}$, and redshifts 0.2 $\lesssim z\lesssim$ 0.9. The total significance of the stacked shear measurement amounts to 54$σ$. We compare cluster masses determined using weak lensing shear and magnification, finding the measureme…
There is currently a discrepancy in the measured value of the amplitude of matter clustering, parameterised using $σ_8$, inferred from galaxy weak lensing, and cosmic microwave background data, which could be an indication of new physics, such as massive neutrinos or a modification to the gravity law, or baryon feedback. In this paper we make the assumption that the cosmological parameters are well determined by Planck, and use weak lensing data to investigate the implications for baryon feedback and massive neutrinos, as well as possible contributions from intrinsic alignments and biases in p…
Higher-order, non-Gaussian aspects of the large-scale structure carry valuable information on structure formation and cosmology, which is complementary to second-order statistics. In this work we measure second- and third-order weak-lensing aperture-mass moments from CFHTLenS and combine those with CMB anisotropy probes. The third moment is measured with a significance of $2σ$. The combined constraint on $Σ_8 = σ_8 (Ω_{\rm m}/0.27)^α$ is improved by 10%, in comparison to the second-order only, and the allowed ranges for $Ω_{\rm m}$ and $σ_8$ are substantially reduced. Including general triangl…
We present the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) that accurately determines a weak gravitational lensing signal from the full 154 square degrees of deep multi-colour data obtained by the CFHT Legacy Survey. Weak gravitational lensing by large-scale structure is widely recognised as one of the most powerful but technically challenging probes of cosmology. We outline the CFHTLenS analysis pipeline, describing how and why every step of the chain from the raw pixel data to the lensing shear and photometric redshift measurement has been revised and improved compared to previo…
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…
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 poin…
This paper presents the first application of 3D cosmic shear to a wide-field weak lensing survey. 3D cosmic shear is a technique that analyses weak lensing in three dimensions using a spherical harmonic approach, and does not bin data in the redshift direction. This is applied to CFHTLenS, a 154 square degree imaging survey with a median redshift of 0.7 and an effective number density of 11 galaxies per square arcminute usable for weak lensing. To account for survey masks we apply a 3D pseudo-Cl approach on weak lensing data, and to avoid uncertainties in the highly non-linear regime, we separ…
We explore the cosmological constraints from cosmic shear using a new way of modelling the non-linear matter correlation functions. The new formalism extends the method of Angulo & White (2010), which manipulates outputs of $N$-body simulations to represent the three-dimensional nonlinear mass distribution in different cosmological scenarios. We show that predictions from our approach for shear two-point correlations at $1$ to $300$ arcmin separations are accurate at the $\sim10$\% level, even for extreme changes in cosmology. For moderate changes, with target cosmologies similar to that prefe…
The Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) comprises deep multi-colour (u*g'r'i'z') photometry spanning 154 square degrees, with accurate photometric redshifts and shape measurements. We demonstrate that the redshift probability distribution function summed over galaxies provides an accurate representation of the galaxy redshift distribution accounting for random and catastrophic errors for galaxies with best fitting photometric redshifts z_p < 1.3. We present cosmological constraints using tomographic weak gravitational lensing by large-scale structure. We use two broad reds…
We present a finely-binned tomographic weak lensing analysis of the Canada-France-Hawaii Telescope Lensing Survey, CFHTLenS, mitigating contamination to the signal from the presence of intrinsic galaxy alignments via the simultaneous fit of a cosmological model and an intrinsic alignment model. CFHTLenS spans 154 square degrees in five optical bands, with accurate shear and photometric redshifts for a galaxy sample with a median redshift of zm =0.70. We estimate the 21 sets of cosmic shear correlation functions associated with six redshift bins, each spanning the angular range of 1.5<theta<35 …
We measure the weak gravitational lensing shear power spectra and their cross-power in two photometric redshift bins from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). The measurements are performed directly in multipole space in terms of adjustable band powers. For the extraction of the band powers from the data we have implemented and extended a quadratic estimator, a maximum likelihood method that allows us to readily take into account irregular survey geometries, masks, and varying sampling densities. We find the 68 per cent credible intervals in the $σ_8$-$Ω_{\rm m}$-plane…
Based on the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), Kilbinger et al. (2013) obtained a constraint on the amplitude of matter fluctuations of $σ_8({Ω_\mathrm{m}}/0.27)^{0.6}=0.79\pm0.03$ from the two-point correlation function (2PCF). This is $\approx3σ$ lower than the value $0.89\pm0.01$ 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. (2015) obtained the higher value of $σ_8({Ω_\mathrm{m}}/0.2…
Reconstruction of the point spread function (PSF) is a critical process in weak lensing measurement. We develop a real-data based and galaxy-oriented pipeline to compare the performances of various PSF reconstruction schemes. Making use of a large amount of the CFHTLenS data, the performances of three classes of interpolating schemes - polynomial, Kriging, and Shepard - are evaluated. We find that polynomial interpolations with optimal orders and domains perform the best. We quantify the effect of the residual PSF reconstruction error on shear recovery in terms of the multiplicative and additi…
We explore an alternative method to the usual shear correlation function approach for the estimation of aperture mass statistics in weak lensing survey data. Our approach builds on the direct estimator method of Schneider (1998). In this paper, to test and validate the methodology, we focus on the aperture mass dispersion. After computing the signal and noise for a weighted set of measured ellipticites we show how the direct estimator can be made into a linear order algorithm that enables a fast and efficient computation. We then investigate the applicability of the direct estimator approach i…
The Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) represents the most powerful weak lensing survey carried out to date. The CFHTLenS (Canada-France-Hawaii Telescope Lensing Survey) team was formed in 2008 to analyse the data from the CFHTLS focussing on a rigorous treatment of systematic effects in shape measurements and photometric redshifts. Here we review the technical challenges that we faced in analysing these data and their solutions which set the current standard for weak lensing analyses. We also present some science highlights that were made possible by this effort including c…
We present the first direct measurement of the galaxy-matter bispectrum as a function of galaxy luminosity, stellar mass, and SED type. Our analysis uses a galaxy-galaxy-galaxy lensing technique (G3L), on angular scales between 9 arcsec to 50 arcmin, to quantify (i) the excess surface mass density around galaxy pairs (excess mass hereafter) and (ii) the excess shear-shear correlations around single galaxies, both of which yield a measure of two types of galaxy-matter bispectra. We apply our method to the state-of-the-art Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), spanning 154 sq…
Weak gravitational lensing is a powerful cosmological probe, with non--Gaussian features potentially containing the majority of the information. We examine constraints on the parameter triplet $(Ω_m,w,σ_8)$ from non-Gaussian features of the weak lensing convergence field, including a set of moments (up to $4^{\rm th}$ order) and Minkowski functionals, using publicly available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of ray--tracing N-body simulations spanning 91 points in $(Ω_m,w,σ_8)$ parameter space, replicating the galaxy sky positions, redshifts and shape noise in the C…
Lensing peaks have been proposed as a useful statistic, containing cosmological information from non-Gaussianities that is inaccessible from traditional two-point statistics such as the power spectrum or two-point correlation functions. Here we examine constraints on cosmological parameters from weak lensing peak counts, using the publicly available data from the 154 deg$^2$ CFHTLenS survey. We utilize a new suite of ray-tracing N-body simulations on a grid of 91 cosmological models, covering broad ranges of the three parameters $Ω_m$, $σ_8$, and $w$, and replicating the Galaxy sky positions, …
We report the first evidence for intrinsic alignment (IA) of red galaxies at $z>1$. We measure the gravitational shear-intrinsic ellipticity (GI) cross-correlation function at $z\sim1.3$ using galaxy positions from the FastSound spectroscopic survey and galaxy shapes from Canada-Hawaii-France telescope lensing survey data. Adopting the non-linear alignment model, we obtain a $2.4σ$-level detection of the IA amplitude $A^{\rm LA}=27.48_{-11.54}^{+11.53}$ (and $2.6σ$ with $A^{\rm LA}=29.43_{-11.49}^{+11.48}$ when weak-lensing contaminations are taken into account), which is larger than the value…
We cross-correlate cosmic microwave background (CMB) lensing and galaxy weak lensing maps using the Planck 2013 and 2015 data and the 154 deg^2 Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). This measurement probes large-scale structure at intermediate redshifts ~0.9, between the high- and low-redshift peaks of the CMB and CFHTLenS lensing kernels, respectively. Using the noise properties of these data sets and standard Planck 2015 LCDM cosmological parameters, we forecast a signal-to-noise ratio ~4.6 for the cross-correlation. We find that the noise level of our actual measurement …
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 s…
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 …
The measurement of cosmic shear using weak gravitational lensing is a challenging task that involves a number of complicated procedures. We study in detail the systematic errors in the measurement of weak lensing Minkowski Functionals (MFs). Specifically, we focus on systematics associated with galaxy shape measurements, photometric redshift errors, and shear calibration correction. We first generate mock weak-lensing catalogs that directly incorporate the actual observational characteristics of the Canada-France-Hawaii Lensing Survey (CFHTLenS). We then perform a Fisher analysis using the lar…
Dark energy may be the first sign of new fundamental physics in the Universe, taking either a physical form or revealing a correction to Einsteinian gravity. Weak gravitational lensing and galaxy peculiar velocities provide complementary probes of General Relativity, and in combination allow us to test modified theories of gravity in a unique way. We perform such an analysis by combining measurements of cosmic shear tomography from the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) with the growth of structure from the WiggleZ Dark Energy Survey and the Six-degree-Field Galaxy Survey…
We present a method to measure the growth of structure and the background geometry of the Universe -- with no a priori assumption about the underlying cosmological model. Using Canada-France-Hawaii Lensing Survey (CFHTLenS) shear data we simultaneously reconstruct the lensing amplitude, the linear intrinsic alignment amplitude, the redshift evolving matter power spectrum, P(k,z), and the co-moving distance, r(z). We find that lensing predominately constrains a single global power spectrum amplitude and several co-moving distance bins. Our approach can localise precise scales and redshifts wher…
We use a range of cosmological data to constrain phenomenological modifications to general relativity on cosmological scales, through modifications to the Poisson and lensing equations. We include cosmic microwave background anisotropy measurements from the Planck satellite, cosmic shear from CFHTLenS and DES-SV, and redshift-space distortions from BOSS data release 12 and the 6dF galaxy survey. We find no evidence of departures from general relativity, with the modified gravity parameters constrained to $Σ_0 = 0.05^{+0.05}_{-0.07}$ and $μ_0 = -0.10^{+0.20}_{-0.16}$, where $Σ_0$ and $μ_0$ refe…
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 fitt…
A likelihood-based method for measuring weak gravitational lensing shear in deep galaxy surveys is described and applied to the Canada-France-Hawaii Telescope (CFHT) Lensing Survey (CFHTLenS). CFHTLenS comprises 154 sq deg of multicolour optical data from the CFHT Legacy Survey, with lensing measurements being made in the i' band to a depth i'(AB)<24.7, for galaxies with signal-to-noise ratio greater than about 10. The method is based on the lensfit algorithm described in earlier papers, but here we describe a full analysis pipeline that takes into account the properties of real surveys. The m…
We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3\% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find $σ_8 (Ω_{\rm m}/0.3)^{0.5} = 0.81 \pm 0.06$ (68\% confidence), after marginalising over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable…
We review the effect of the commonly-used Limber and flat-sky approximations on the calculation of shear power spectra and correlation functions for galaxy weak lensing. These approximations are accurate at small scales, but it has been claimed recently that their impact on low multipoles could lead to an increase in the amplitude of the mass fluctuations inferred from surveys such as CFHTLenS, reducing the tension between galaxy weak lensing and the amplitude determined by Planck from observations of the cosmic microwave background. Here, we explore the impact of these approximations on cosmo…
We present current and future constraints on equations of state for dark sector perturbations. The equations of state considered are those corresponding to a generalized scalar field model and time-diffeomorphism invariant $L(g)$ theories that are equivalent to models of a relativistic elastic medium and also Lorentz violating massive gravity. We develop a theoretical understanding of the observable impact of these models. In order to constrain these models we use CMB temperature data from Planck, BAO measurements, CMB lensing data from Planck and the South Pole Telescope, and weak galaxy lens…
Within the standard LCDM model of cosmology, the recent Planck measurements have shown discrepancies with other observations, e.g., measurements of the current expansion rate H_0, the galaxy shear power spectrum and counts of galaxy clusters. We show that if LCDM is extended by a hot dark matter component, which could be interpreted as a sterile neutrino, the data sets can be combined consistently. A combination of Planck data, WMAP-9 polarisation data, measurements of the BAO scale, the HST measurement of H_0, Planck galaxy cluster counts and galaxy shear data from the CFHTLens survey yields …
In this manuscript of the habilitation à diriger des recherches (HDR), the author presents some of his work over the last ten years. The main topic of this thesis is cosmic shear, the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Univer…
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 lar…
We investigate the sensitivity to the effects of lensing magnification on large-scale structure analyses combining photometric cosmic shear and galaxy clustering data (i.e. the now commonly called "3$\times$2-point" analysis). Using a Fisher matrix bias formalism, we disentangle the contribution to the bias on cosmological parameters caused by ignoring the effects of magnification in a theory fit from individual elements in the data vector, for Stage-III and Stage-IV surveys, assuming well-known redshift distributions, sample selection based on magnitude, and magnification strengths inferred f…
We show that dust absorption in disk galaxies leads to a color- and orientation-dependent centroid shift which is expected to be observable in multi-band imaging surveys. This centroid shift is an interesting new probe which contains astrophysically and cosmologically relevant information: it can be used to probe the dust content of a large sample of galaxies, and to reduce the shape noise due to inclination of disk galaxies for weak lensing shear. Specifically, we find that data sets comparable to CFHTLenS, the Dark Energy Survey (DES) or the Hyper Suprime-Cam (HSC) survey should provide a du…
We investigate the problem of noise bias in maximum likelihood and maximum a posteriori estimators for cosmic shear. We derive the leading and next-to-leading order biases and compute them in the context of galaxy ellipticity measurements, extending previous work on maximum likelihood inference for weak lensing. We show that a large part of the bias on these point estimators can be removed using information already contained in the likelihood when a galaxy model is specified, without the need for external calibration. We test these bias-corrected estimators on simulated galaxy images similar t…
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next apply the approach to estimation of shear lensing, closely followi…
(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $σ_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that …
In this paper, we motivate the use of galaxy clustering measurements using photometric redshift information, including a contribution from flux magnification, as a probe of cosmology. We present cosmological forecasts when clustering data alone is used, and when clustering is combined with a cosmic shear analysis. We consider two types of clustering analysis: firstly, clustering with only redshift auto-correlations in tomographic redshift bins; secondly, using all available redshift bin correlations. Finally, we consider how inferred cosmological parameters may be biased using each analysis wh…
We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a dataset, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of datapoints which depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnostic, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation function…
We present and describe im3shape, a new publicly available galaxy shape measurement code for weak gravitational lensing shear. im3shape performs a maximum likelihood fit of a bulge-plus-disc galaxy model to noisy images, incorporating an applied point spread function. We detail challenges faced and choices made in its design and implementation, and then discuss various limitations that affect this and other maximum likelihood methods. We assess the bias arising from fitting an incorrect galaxy model using simple noise-free images and find that it should not be a concern for current cosmic shea…
We present a derivation of a generalized optimally-weighted estimator for the weak lensing magnification signal, including a calculation of errors. With this estimator, we present a local method for optimally estimating the local effects of magnification from weak gravitational lensing, using a comparison of number counts in an arbitrary region of space to the expected unmagnified number counts. We show that when equivalent lens and source samples are used, this estimator is simply related to the optimally-weighted correlation function estimator used in past work and vice-versa, but this metho…
Density-estimation likelihood-free inference (DELFI) has recently been proposed as an efficient method for simulation-based cosmological parameter inference. Compared to the standard likelihood-based Markov Chain Monte Carlo (MCMC) approach, DELFI has several advantages: it is highly parallelizable, there is no need to assume a possibly incorrect functional form for the likelihood and complicated effects (e.g the mask and detector systematics) are easier to handle with forward models. In light of this, we present two DELFI pipelines to perform weak lensing parameter inference with lognormal re…
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-…
We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in one-dimensional posteriors of $Ω_{\rm m}$ and $σ_{\rm 8}$ due to the non-Gaussian likelihood distributions of shear …
The intrinsic scatter in the ellipticities of galaxies about the mean shape, known as "shape noise," is the most important source of noise in weak lensing shear measurements. Several approaches to reducing shape noise have recently been put forward, using information beyond photometry, such as radio polarization and optical spectroscopy. Here we investigate how well the intrinsic ellipticities of galaxies can be predicted using other, exclusively photometric parameters. These parameters (such as galaxy colours) are already available in the data and do not necessitate additional, often expensiv…
We derive the essentials of the skewed weak lensing likelihood via a simple Hierarchical Model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing analyses are naturally biased low, and this does not indicate any new physics such as deviations from $Λ$CDM. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from CMB analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected …
The number of observed dwarf galaxies, with dark matter mass $\lesssim 10^{11}$ M$_{\odot}$ in the Milky Way or the Andromeda galaxy does not agree with predictions from the successful $Λ$CDM paradigm. To alleviate this problem a suppression of dark matter clustering power on very small scales has been conjectured. However, the abundance of dark matter halos outside our immediate neighbourhood (the Local Group) seem to agree with the $Λ$CDM--expected abundance. Here we connect these problems to observations of weak lensing cosmic shear, pointing out that cosmic shear can make significant state…
The high sensitivity of the new generation of radio telescopes such as the Square Kilometre Array (SKA) will allow cosmological weak lensing measurements at radio wavelengths that are competitive with optical surveys. We present an adaptation to radio data of lensfit, a method for galaxy shape measurement originally developed and used for optical weak lensing surveys. This likelihood method uses an analytical galaxy model and makes a Bayesian marginalisation of the likelihood over uninteresting parameters. It has the feature of working directly in the visibility domain, which is the natural ap…
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 obser…
We present the optimal convergence and shear estimators for lensing reconstruction from the cosmic microwave background temperature field. This generalizes the deflection estimator, is sensitive to non-lensing modes, provides internal consistency checks, and is always at least as optimal. Previously, these estimators were only known in the squeezed limit. This paper decomposes convergence and shear fields into cosine and sine waves and the lensed correlation function is then Taylor expanded in the wave amplitudes. Maximizing the likelihood function gives the optimal estimators for the converge…
Cosmic shear is considered one of the most powerful methods for studying the properties of Dark Energy in the Universe. As a standard method, the two-point correlation functions $xi_\pm(theta)$ of the cosmic shear field are used as statistical measures for the shear field. In order to separate the observed shear into E- and B-modes, the latter being most likely produced by remaining systematics in the data set and/or intrinsic alignment effects, several statistics have been defined before. Here we aim at a complete E-/B-mode decomposition of the cosmic shear information contained in the $xi_\p…
