Cosmic Shear Research Articles

Nonparametric cosmology with cosmic shear

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 where Lambda-Cold Dark Matter (LCDM) fails -- if any. We find that below z = 0.4, the measured co-moving distance r (z) is higher than that expected from the Planck LCDM cosmology by ~1.5 sigma, while at higher redshifts, our reconstruction is fully consistent. To validate our reconstruction, we compare LCDM parameter constraints from the standard cosmic shear likelihood analysis to those found by fitting to the non-parametric information and we find good agreement.

Cosmic convergence and shear with extended sources

The standard theory of weak gravitational lensing relies on the approximation that light beams are infinitesimal. Our recent work showed that the finite size of sources, and the associated light beams, can cause nonperturbative corrections to the weak-lensing convergence and shear. This article thoroughly investigates these corrections in a realistic cosmological model. The continuous transition from infinitesimal to finite beams is understood, and reveals that the previous results overestimated finite-beam effects due to simplistic assumptions on the distribution of matter in the Universe. In a KiloDegree Survey-like setting, finite-beam corrections to the cosmic shear remain subpercent, while percent-level corrections are only reached on subarcmin scales. This article thus demonstrates the validity of the infinitesimal-beam approximation in the interpretation of current weak-lensing data.

Dark Energy Survey Year 1: An independent E/B-mode cosmic shear analysis

Abstract We present an independent cosmic shear analysis of the non-cosmological B-mode distortions within the public first year data from the Dark Energy Survey (DES). We find no significant detection of B-modes in a full tomographic analysis of the primary metacalibrationshear catalogue. This is in contrast to the secondary im3shapeshear catalogue, where we detect B-modes at a significance of ∼3σ with a pattern that is consistent with the B-mode signature of a repeating additive shear bias across the survey. We use the COSEBIs statistic to cleanly separate the B-modes from the gravitational lensing signal (E-modes). We find good agreement between the measured E-modes and their theoretical expectation given the DES cosmological parameter constraints.

Constraints on Cosmology and Baryonic Feedback with the Deep Lens Survey Using Galaxy–Galaxy and Galaxy–Mass Power Spectra

Abstract We present cosmological parameter measurements from the Deep Lens Survey (DLS) using galaxy–mass and galaxy–galaxy power spectra in the multipole range ℓ = 250–2000. We measure galaxy–galaxy power spectra from two lens bins centered at z ∼ 0.27 and 0.54 and galaxy–mass power spectra by cross-correlating the positions of galaxies in these two lens bins with galaxy shapes in two source bins centered at z ∼ 0.64 and 1.1. We marginalize over a baryonic feedback process using a single-parameter representation and a sum of neutrino masses, as well as photometric redshift and shear calibration systematic uncertainties. For a flat ΛCDM cosmology, we determine , in good agreement with our previous DLS cosmic shear and the Planck cosmic microwave background (CMB) measurements. Without the baryonic feedback marginalization, S 8 decreases by because the dark-matter-only power spectrum lacks the suppression at the highest ℓ values owing to active galactic nucleus (AGN) feedback. Together with the Planck CMB measurements, we constrain the baryonic feedback parameter to , which suggests an interesting possibility that the actual AGN feedback might be stronger than the recipe used in the OverWhelmingly Large cosmological hydrodynamical Simulations. The interpretation is limited by the validity of the baryonic feedback simulation and the one-parameter representation of the effect.

Weak-lensing shear measurement with machine learning

Cosmic shear, that is weak gravitational lensing by the large-scale matter structure of the Universe, is a primary cosmological probe for several present and upcoming surveys investigating dark matter and dark energy, such as Euclid or WFIRST. The probe requires an extremely accurate measurement of the shapes of millions of galaxies based on imaging data. Crucially, the shear measurement must address and compensate for a range of interwoven nuisance effects related to the instrument optics and detector, noise in the images, unknown galaxy morphologies, colors, blending of sources, and selection effects. This paper explores the use of supervised machine learning as a tool to solve this inverse problem. We present a simple architecture that learns to regress shear point estimates and weights via shallow artificial neural networks. The networks are trained on simulations of the forward observing process, and take combinations of moments of the galaxy images as inputs. A challenging peculiarity of the shear measurement task, in terms of machine learning applications, is the combination of the noisiness of the input features and the requirements on the statistical accuracy of the inverse regression. To address this issue, the proposed training algorithm minimizes bias over multiple realizations of individual source galaxies, reducing the sensitivity to properties of the overall sample of source galaxies. Importantly, an observational selection function of these source galaxies can be straightforwardly taken into account via the weights. We first introduce key aspects of our approach using toy-model simulations, and then demonstrate its potential on images mimicking Euclid data. Finally, we analyze images from the GREAT3 challenge, obtaining competitively low multiplicative and additive shear biases despite the use of a simple training set. We conclude that the further development of suited machine learning approaches is of high interest to meet the stringent requirements on the shear measurement in current and future surveys. We make a demonstration implementation of our technique publicly available.

Real-space computation of E/B-mode maps. Part I. Formalism, compact kernels, and polarized filaments

We derive full-sky, real-space operators that convert between polarization Stokes Q/U parameters and the coordinate-independent scalar E/B modes that are widely used in Cosmic Microwave Background (CMB) and cosmic shear analysis. We also derive real space operators that decompose the measured Stokes parameters into those corresponding to E-modes and B-modes respectively, without ever evaluating the scalar fields themselves. We cast the standard CMB polarization analysis operators in a matrix-vector notation which elucidates these derivations. For all these real space operators we show that the kernels split naturally into angular and radial parts and we show explicitly how the radial extent of these kernels depends on the targeted band-limit. We show that the kernels can be interpreted either as a complex convolving beam or as a Green's function when they are expressed in terms of the forward or inverse rotation Euler angles. We show that an arbitrary radial function can produce E/B-like maps, provided it vanishes at the origin and the antipodal point. These maps are simply filtered versions of the standard E/B maps. We can recover the standard power spectrum of the polarized CMB sky by correcting the power spectra of these maps with a simple window function, which we show how to derive for any radial dependence. For these reasons we can compute E/B maps in real space with a compactly-supported kernel, an approach that can guarantee the avoidance of known foreground regions and could be employed in a massively-parallel scheme at high-resolution. We show that the spin raising and lowering operators ð2/ð2 are special cases of these generalized radial functions, and present their band limited versions. The spatial structure of the real space operators provides great intuition for the E/B structure of polarized, filamentary galactic foregrounds. We predict a non-zero B-mode signature that is expected from polarized filaments in the sky. This paper is the first part in a series of papers that explore real-space computation of polarization modes and their applications.

Mapping the universe with dark energy survey

First, I summarize the current status of dark energy, including methods to use data to separate between general-relativity and modified-gravity scenarios for the accelerating universe. Then, I discuss recent results from the Dark Energy Survey, currently the world’s leading experiment mapping large-scale structure in the universe. Year-1 DES analysis performed in 2017 included the combination of galaxy clustering, cosmic shear, and their cross-correlation to impose constraints on key cosmological parameters, while upcoming Year-3 and -5 analyses will dramatically improve those constraints. I discuss some of the challenges in this complex analysis, its results, and the more general path forward toward better understanding of dark matter and dark energy in the universe. I also comment on the foremost tension in the field of cosmology today: between local measurements of the Hubble constant from type Ia supernovae, and global measurements from the cosmic microwave background anisotropies.

Does quartessence ease cosmic tensions?

Tensions between cosmic microwave background observations and the growth of the large-scale structure inferred from late-time probes pose a serious challenge to the concordance $\Lambda$CDM cosmological model. State-of-the-art data from the Planck satellite predicts a higher rate of structure growth than what preferred by low-redshift observables. Such tension has hitherto eluded conclusive explanations in terms of straightforward modifications to $\Lambda$CDM, e.g. the inclusion of massive neutrinos or a dynamical dark energy component. Here, we investigate models of 'quartessence' -- a single dark component mimicking both dark matter and dark energy -- whose non-vanishing sound speed inhibits structure growth at late times on scales smaller than its corresponding Jeans' length. In principle, this could reconcile high- and low-redshift observations. We put this hypothesis to test against temperature and polarisation spectra from the latest Planck release, SDSS DR12 measurements of baryon acoustic oscillations and redshift-space distortions, and cosmic shear correlation functions from KiDS. This the first time that any specific model of quartessence is applied to actual data. We show that, if we naively apply $\Lambda$CDM nonlinear prescription to quartessence, the combined data sets allow for tight constraints on the model parameters. Apparently, quartessence alleviates the tension between the total matter fraction and late-time structure clustering, although in fact the tension is transferred from the latter to the quartessence sound speed parameter. However, we found that this strongly depends upon information from nonlinear scales. Indeed, if we relax this assumption, quartessence models appear still viable. For this reason, we argue that the nonlinear behaviour of quartessence deserves further investigation and may lead to a deeper understanding of the physics of the dark Universe.

Self-calibration method for II and GI types of intrinsic alignments of galaxies

We introduce a self-calibration method that can be applied to the intrinsic ellipticity--intrinsic ellipticity (II) and gravitational shear -- intrinsic ellipticity (GI) types of intrinsic alignment of galaxies. The method combines previous self-calibration techniques with modifications to one of them in order to use auto-spectra in addition to cross-spectra between redshift bins. This allows one to use the self-calibration while preserving all the constraining power of cosmic shear from surveys. We show that the new method provides more flexibility in using various redshift bin widths. We perform cosmological parameter constraint forecast when this method is applied to the Large Synoptic Survey Telescope (LSST). Compared to the original self-calibration, we find that the new method provides further significant reduction in any residual shift in the cosmological parameters (e.g. factors of $2-4$ for the dark energy equation of state) which is promising for accurate cosmology.

Investigating scalar-tensor-gravity with statistics of the cosmic large-scale structure

Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy component, and the addition of neutrinos changing structures on small scales. Here we study Horndeski theories of gravity, the most general minimally coupled scalar-tensor theories of second order. While the cosmological background evolution can be described by an effective equation of state, the perturbations are characterised by four free functions of time. We consider a specific parametrisation of these functions tracing the dark energy component. The likelihood of the full parameter set resulting from combining cosmic microwave background primary anisotropies including their gravitational lensing signal, tomographic angular galaxy clustering and weak cosmic shear, together with all possible non-vanishing cross-correlations is evaluated; both with the Fisher-formalism as well as without the assumption of a specific functional form of the posterior through Monte-Carlo Markov-chains (MCMCs). Our results show that even complex cosmological models can be constrained and could exclude variations of the effective Newtonian gravitational coupling larger than 10\% over the age of the Universe. In particular, we confirm strong correlations between parameter groups. Furthermore, we find that the expected contours from MCMC are significantly larger than those from the Fisher analysis even with the vast amount of signal provided by stage IV experiments, illustrating the importance of a proper treatment of non-Gaussian likelihoods and the high level of precision needed for unlocking the sensitivity on gravitational parameters.

Lenstronomy: Multi-purpose gravitational lens modelling software package

We present lenstronomy, a multi-purpose open-source gravitational lens modelling pythonpackage. lenstronomy is able to reconstruct the lens mass and surface brightness distributions of strong lensing systems using forward modelling. lenstronomy supports a wide range of analytic lens and light models in arbitrary combination. The software is also able to reconstruct complex extended sources (Birrer et. al 2015) as well as being able to model point sources. We designed lenstronomy to be stable, flexible and numerically accurate, with a clear user interface that could be deployed across different platforms. Throughout its development, we have actively used lenstronomy to make several measurements including deriving constraints on dark matter properties in strong lenses, measuring the expansion history of the universe with time-delay cosmography, measuring cosmic shear with Einstein rings and decomposing quasar and host galaxy light. The software is distributed under the MIT license. The documentation, starter guide, example notebooks, source code and installation guidelines can be found at https://lenstronomy.readthedocs.io.

3D cosmic shear: Numerical challenges, 3D lensing random fields generation, and Minkowski functionals for cosmological inference

Cosmic shear - the weak gravitational lensing effect generated by fluctuations of the gravitational tidal fields of the large-scale structure - is one of the most promising tools for current and future cosmological analyses. The spherical-Bessel decomposition of the cosmic shear field ("3D cosmic shear") is one way to maximise the amount of redshift information in a lensing analysis and therefore provides a powerful tool to investigate in particular the growth of cosmic structure that is crucial for dark energy studies. However, the computation of simulated 3D cosmic shear covariance matrices presents numerical difficulties, due to the required integrations over highly oscillatory functions. We present and compare two numerical methods and relative implementations to perform these integrations. We then show how to generate 3D Gaussian random fields on the sky in spherical coordinates, starting from the 3D cosmic shear covariances. To validate our field-generation procedure, we calculate the Minkowski functionals associated with our random fields, compare them with the known expectation values for the Gaussian case and demonstrate parameter inference from Minkowski functionals from a cosmic shear survey. This is a first step towards producing fully 3D Minkowski functionals for a lognormal field in 3D to extract Gaussian and non-Gaussian information from the cosmic shear field, as well as towards the use of Minkowski functionals as a probe of cosmology beyond the commonly used two-point statistics.

Covariances for cosmic shear and galaxy–galaxy lensing in the response approach

In this study, we measure the response of matter and halo projected power spectra $P^{\rm 2D}_{\rm XY}(k)$ (X, Y are matter and/or halos), to a large-scale density contrast, $\delta_{\rm b}$, using separate universe simulations. We show that the fractional response functions, i.e., $\mathrm{d}\ln P^{\rm 2D}_{\rm XY}(k)/\mathrm{d}\delta_{\rm b}$, are identical to their respective three-dimensional power spectra within simulation measurement errors. Then, using various $N$-body simulation combinations (small-box simulations with periodic boundary conditions and sub-volumes of large-box simulations) to construct {mock observations of projected fields}, we study how super-survey modes, in both parallel and perpendicular directions to the projection direction, affect the covariance matrix of $P^{\rm 2D}_{\rm XY}(k)$, known as super-sample covariance (SSC). Our results indicate that the SSC term provides dominant contributions to the covariances of matter-matter and matter-halo spectra at small scales but does not provide significant contributions in the halo-halo spectrum. We observe that the large-scale density contrast in each redshift shell causes most of the SSC effect, and we did not observe a SSC signature arising from large-scale tidal field within the levels of measurement accuracy. We also develop a response approach to calibrate the SSC term for cosmic shear correlation function and galaxy--galaxy weak lensing, and validate the method by comparison with the light-cone ray-tracing simulations. Our method provides a reasonably accurate, albeit computationally inexpensive, way to calibrate the covariance matrix for clustering observables available from wide-area galaxy surveys.

Exploring the Tension between Current Cosmic Microwave Background and Cosmic Shear Data

This paper provides a snapshot of the formal S 8 ≡ σ 8 Ω m / 0.3 tension between Planck 2015 and the Kilo Degree Survey of450 deg 2 of imaging data (KiDS-450) or the Canada France Hawaii Lensing Survey (CFHTLenS). We find that the Cosmic Microwave Bckground (CMB) and cosmic shear datasets are in tension in the standard Λ Cold Dark Matter ( Λ CDM) model, and that adding massive neutrinos does not relieve the tension. If we include an additional scaling parameter on the CMB lensing amplitude A l e n s , we find that this can put in agreement the Planck 2015 with the cosmic shear data. A l e n s is a phenomenological parameter that is found to be more than 2 σ higher than the expected value in the Planck 2015 data, suggesting an higher amount of lensing in the power spectra, not supported by the trispectrum analysis.

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.

Deep lensing with a twist: E and B modes in a field with multiple lenses

We explore the weak lensing E- and B-mode shear signals of a field of galaxy clusters using both large scale structure N-body simulations and multi-color Suprime-cam & Hubble Space Telescope observations. Using the ray-traced and observed shears along with photometric redshift catalogs, we generate mass maps of the foreground overdensities by optimally filtering the tangential shear that they induce on background galaxies. We then develop and test a method to approximate the foreground structure as a superposition of NFW-like halos by locating these overdensities and determining their mass and redshift, thereby modeling the background correlated shear field as a sum of lensings induced by the foreground clusters. We demonstrate that the B-mode maps and shear correlation functions, which are generated by similarly filtering the cross shear in this method, are in agreement with observations and are related to the estimated cluster masses and locations as well as the distribution of background sources. Using the foreground mass model, we identify several sources of weak lensing B-modes including leakage and edge effects, source clustering, and multiple lensing which can be observed in deep cosmic shear surveys.

K -cut cosmic shear: Tunable power spectrum sensitivity to test gravity

If left unchecked modeling uncertainties at small scales, due to poorly understood baryonic physics and non-linear structure formation, will significantly bias Stage IV cosmic shear two-point statistic parameter constraints. While it is perhaps possible to run N-body or hydrodynamical simulations to determine the impact of these effects this approach is computationally expensive; especially to test a large number of theories of gravity. Instead we propose directly removing sensitivity to small-scale structure from the lensing spectrum, creating a statistic that is robust to these uncertainties. We do this by taking a redshift-dependent l-cut after applying the Bernardeau-Nishimichi-Taruya (BNT) nulling scheme. This reorganizes the information in the lensing spectrum to make the relationship between the angular scale, l, and the structure scale, k, much clearer compared to standard cosmic shear power spectra -- for which no direct relationship exists. We quantify the effectiveness of this method at removing sensitivity to small scales and compute the predicted Fisher error on the dark energy equation of state, w0, for different k-cuts in the matter power spectrum.

Accurate cosmic shear errors: do we need ensembles of simulations?

Accurate inference of cosmology from weak lensing shear requires an accurate shear power spectrum covariance matrix. Here, we investigate this accuracy requirement and quantify the relative importance of the Gaussian (G), super-sample covariance (SSC) and connected non-Gaussian (cNG) contributions to the covariance. Specifically, we forecast cosmological parameter constraints for future wide-field surveys and study how different covariance matrix components affect parameter bounds. Our main result is that the cNG term represents only a small and potentially negligible contribution to statistical parameter errors: the errors obtained using the G+SSC subset are within ≲ 5% of those obtained with the full G+SSC+cNG matrix for a Euclid-like survey. This result also holds for the shear two-point correlation function, variations in survey specifications and for different analytical prescriptions of the cNG term. The cNG term is that which is often tackled using numerically expensive ensembles of survey realizations. Our results suggest however that the accuracy of analytical or approximate numerical methods to compute the cNG term is likely to be sufficient for cosmic shear inference from the next generation of surveys.

The effects of calibration on the bias of shear measurements

Forthcoming large-scale surveys will soon attempt to measure cosmic shear to an unprecedented level of accuracy, requiring a similarly high level of accuracy in the shear measurements of galaxies. Factors such as pixelisation, imperfect point-spread function (PSF) correction, and pixel noise can all directly or indirectly lead to biases in shear measurements, and so it can be necessary for shear measurement methods to be calibrated against internal, external, or simulated data to minimize bias. It is thus important to understand the nature of this calibration. In this paper, we show that a typical calibration procedure will on average leave no residual additive bias, but will leave a residual multiplicative bias. Additionally, the errors on the post-calibration bias parameters will be changed, and on average increased, from the errors on the pre-calibration measurements of these parameters, but that this is generally worth the benefit in decreasing the expected value of the multiplicative bias. We find that in most typical cases, it is worthwhile to apply a first-order bias correction, while a higher-order bias correction is only worthwhile for methods with intrinsically high multiplicative bias ($>10$ per cent) or when the simulation size is very small ($<10^6$ simulated galaxies).

Beyond the traditional line-of-sight approach of cosmological angular statistics

We present a new efficient method to compute the angular power spectra of large-scale structure observables that circumvents the numerical integration over Bessel functions, expanding on a recently proposed algorithm based on FFTlog. This new approach has better convergence properties. The method is explicitly implemented in the CLASS code for the case of number count Cℓ's (including redshift-space distortions, weak lensing, and all other relativistic corrections) and cosmic shear Cℓ's. In both cases our approach speeds up the calculation of the exact Cℓ's (without the Limber approximation) by a factor of order 400 at a fixed precision target of 0.1%.