In this paper we show how response function corrections to shear measurements (e.g. as required by Metacalibration) propagate into cosmic shear power spectra. We investigate a 2-sphere pixel (also known as HEALpixel') correction and a forward-modelling approach using simple Gaussian simulations. In the 2-sphere pixel-correction approach we find a free parameter that is the tolerated condition number of the local response matrices: if this is too large then this can cause an amplification of the shot noise power spectrum, if too small it can lead to a loss of area (and a possible selection bias). In contrast by forward-modelling the power spectrum this choice can be avoided. This also applies to map-based inference methods using shear-response calibrated maps.
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…
We introduce the Generalised Lensing and Shear Spectra GLaSS code which is available for download from https://github.com/astro-informatics/GLaSS It is a fast and flexible public code, written in Python, that computes generalized spherical cosmic shear spectra. The commonly used tomographic and spherical Bessel lensing spectra come as built-in run-mode options. GLaSS is integrated into the Cosmosis modular cosmological pipeline package. We outline several computational choices that accelerate the computation of cosmic shear power spectra. Using GLaSS, we test whether the assumption that using …
We infer gravitational lensing shear and convergence fields from galaxy ellipticity catalogs under a spatial process prior for the lensing potential. We demonstrate the performance of our algorithm with simulated Gaussian-distributed cosmological lensing shear maps and a reconstruction of the mass distribution of the merging galaxy cluster Abell 781 using galaxy ellipticities measured with the Deep Lens Survey. Given interim posterior samples of lensing shear or convergence fields on the sky, we describe an algorithm to infer cosmological parameters via lens field marginalization. In the most …
Highly precise weak lensing shear measurement is required for statistical weak gravitational lensing analysis such as cosmic shear measurement to achieve severe constrain on the cosmological parameters. For this purpose any systematic error in the measurement should be corrected. One of the main systematic error comes from Pixel noise which is Poisson noise of flux from atmosphere. We investigate how the pixel noise makes systematic error in shear measurement based on ERA method and develop the correction method. This method is tested by simulations with various conditions and it is confirmed …
Current optical imaging surveys for cosmology are covering large areas of sky. To exploit the statistical power of these surveys for weak lensing measurements requires shape measurement methods with subpercent systematic errors. We introduce a new weak lensing shear measurement algorithm, Shear Nulling after PSF Gaussianisation (SNAPG), designed to avoid the noise biases that affect most other methods. SNAPG operates on images that have been convolved with a kernel that renders the Point Spread Function (PSF) a circular Gaussian, and uses weighted second moments of the sources. The response of…
We have developed a new technique called Direct Shear Mapping (DSM) to measure gravitational lensing shear directly from observations of a single background source. The technique assumes the velocity map of an un-lensed, stably-rotating galaxy will be rotationally symmetric. Lensing distorts the velocity map making it asymmetric. The degree of lensing can be inferred by determining the transformation required to restore axisymmetry. This technique is in contrast to traditional weak lensing methods, which require averaging an ensemble of background galaxy ellipticity measurements, to obtain a s…
Highly precise weak lensing shear measurement is required for statistical weak gravitational lensing analysis such as cosmic shear measurement to achieve severe constraint on the cosmological parameters. For this purpose, the accurate shape measurement of background galaxies is absolutely important in which any systematic error in the measurement should be carefully corrected. One of the main systematic error comes from photon noise which is Poisson noise of flux from the atmosphere(noise bias). We investigate how the photon noise makes a systematic error in shear measurement within the framew…
CMB lensing from current and upcoming wide-field CMB experiments such as AdvACT, SPT-3G and Simons Observatory relies heavily on temperature (vs. polarization). In this regime, foreground contamination to the temperature map produces significant lensing biases, which cannot be fully controlled by multi-frequency component separation, masking or bias hardening. In this letter, we split the standard CMB lensing quadratic estimator into a new set of optimal "multipole" estimators. On large scales, these multipole estimators reduce to the known magnification and shear estimators, and a new shear B…
Weak lensing has become an increasingly important tool in cosmology and the use of galaxy shapes to measure cosmic shear has become routine. The weak-lensing distortion tensor contains two other effects in addition to the two components of shear: the convergence and rotation. The rotation mode is not measurable using the standard cosmic shear estimators based on galaxy shapes, as there is no information on the original shapes of the images before they were lensed. Due to this, no estimator has been proposed for the rotation mode in cosmological weak-lensing surveys, and the rotation mode has n…
We have investigated, using both a theoretical and an empirical approach, the frequency of low redshift galaxy-galaxy lensing systems in which the signature of weak lensing might be directly detectable. We find good agreement between these two approaches. In order to make a theoretical estimate of the weak lensing shear, $γ$, for each galaxy in a catalogue, we have made an estimate of the asymptotic circular velocity from the stellar mass using three different approaches: from a simulation based relation, from an empirically-derived relation, and using the baryonic Tully-Fisher relation. Using…
We present a combined cosmic shear analysis of the modeling of line-of-sight distortions on strongly lensed extended arcs and galaxy shape measurements in the COSMOS field. We develop a framework to predict the covariance of strong lensing and galaxy shape measurements of cosmic shear on the basis of the small scale matter power-spectrum. The weak lensing measurement is performed using data from the COSMOS survey calibrated with a cloning scheme using the Ultra Fast Image Generator UFig (Berge 2013). The strong lensing analysis is performed by forward modeling the lensing arcs with a main lens…
The magnification of galaxies in modern galaxy surveys induces additional correlations in the cosmic shear, galaxy-galaxy lensing and clustering observables used in modern lensing "3x2pt" analyses, due to sample selection. In this paper, we emulate the magnification contribution to all three observables utilising the SLICS simulations suite, and test the sensitivity of the cosmological model, galaxy bias and redshift distribution calibration to un-modelled magnification in a Stage-IV-like survey using Monte-Carlo sampling. We find that magnification cannot be ignored in any single or combined …
We developed a new method that uses ellipticity defined by 0th order moments (0th-ellipticity) for weak gravitational lensing shear analysis. Although there is a strong correlation between the ellipticity calculated using this approach and the usual ellipticity defined by the 2nd order moment, the ellipticity calculated here has a higher signal-to-noise ratio because it is weighted to the central region of the image. These results were confirmed using data for Abell 1689 from the Subaru telescope. For shear analysis, we adopted the ellipticity of re-smeared artificial image (ERA) method for po…
Weak lensing shear estimation typically results in per galaxy statistical errors significantly larger than the sought after gravitational signal of only a few percent. These statistical errors are mostly a result of shape-noise -- an estimation error due to the diverse (and a-priori unknown) morphology of individual background galaxies. These errors are inversely proportional to the limiting angular resolution at which localized objects, such as galaxy clusters, can be probed with weak lensing shear. In this work we report on our initial attempt to reduce statistical errors in weak lensing she…
The next generation weak lensing surveys (i.e., LSST, Euclid and WFIRST) will require exquisite control over systematic effects. In this paper, we address shear calibration and present the most realistic forecast to date for LSST/Euclid/WFIRST and CMB lensing from a stage 4 CMB experiment (CMB S4). We use the CosmoLike code to simulate a joint analysis of all the two-point functions of galaxy density, galaxy shear and CMB lensing convergence. We include the full Gaussian and non-Gaussian covariances and explore the resulting joint likelihood with Monte Carlo Markov Chains. We constrain shear c…
An excess up-scattering mass bias on a weak lensing cluster mass estimate is a statistical bias that an observed weak lensing mass ($M_{\rm obs}$) of a cluster of galaxies is, in a statistical sense, larger than its true mass ($M_{\rm true}$) because of a higher chance of up-scattering than that of down-scattering due to random noises in a weak lensing cluster shear profile. This non-symmetric scattering probability is caused by a monotonically decreasing cluster mass function with increasing mass. We examine this bias (defined by $b=M_{\rm obs}/M_{\rm true}$) in weak lensing shear-selected cl…
We quantify the cosmological constraining power of the `lensing PDF' - the one-point probability density of weak lensing convergence maps - by modelling this statistic numerically with an emulator trained on $w$CDM cosmic shear simulations. After validating our methods on Gaussian and lognormal fields, we show that `multi-scale' PDFs - measured from maps with multiple levels of smoothing - offer considerable gains over two-point statistics, owing to their ability to extract non-Gaussian information: for a mock Stage-III survey, lensing PDFs yield 33\% tighter constraints on the clustering para…
We improve the ERA(Ellipticity of Re-smeared Artificial image) method of PSF(Point Spread Function) correction in weak lensing shear analysis in order to treat realistic shape of galaxies and PSF. This is done by re-smearing PSF and the observed galaxy image smeared by a RSF(Re-Smearing Function), and allows us to use a new PSF with a simple shape and to correct PSF effect without any approximations and assumptions. We perform numerical test to show that the method applied for galaxies and PSF with some complicated shapes can correct PSF effect with systematic error less than 0.1%. We also app…
A systematic study of projection biases in the Weak Lensing analysis of cosmic shear and the combination of galaxy clustering and galaxy-galaxy lensing
We derive a new relation between cosological distances, valid in any (statistically) isotropic space-time and independent of cosmological parameters or even the validity of the field equation of General Relativity. In particular, this relation yields an equation between those distance ratios which are the geometrical factors determining the strength of the gravitational lensing effect of mass concentrations. Considering a combination of weak lensing shear ratios, based on lenses at two different redshifts, and sources at three different redshifts, we derive a relation between shear-ratio tests…
The Shear-to-Cosmology Paradigm I. Hybrid Field-Level and Simulation-Based Framework for Weak Lensing Surveys
Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；School of Physics and Astronomy, Sun Yat-Sen University（中山大学物理学院）；CSST Science Center for the Guangdong–Hong Kong–Macau Greater Bay Area, SYSU（中山大学嫦娥四号科学中心粤港澳大湾区分中心）
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…
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 …
Weak gravitational lensing flexions are a kind of weak lensing distortion which are defined as the spin 1 and spin 3 combinations of the third order derivatives of gravitational lensing potential. Since the shear has spin 2 combination of the second order derivative, the flexion signal gives a partly independent information from shear signal and is more sensitive to the local mass distribution than shear signal. Thus its measurement is expected to play important roles in observational cosmology. However, since the weakness of the flexion signal as well as the complicatedness of its intrinsic n…
Weak-Lensing Shear Response for Photometric Redshift-Based Tomographic Binning
Brookhaven National Laboratory（布鲁海文国家实验室）；University of Pittsburgh（匹兹堡大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Carnegie Mellon University（卡内基梅隆大学）
We propose a new mass-mapping algorithm, specifically designed to recover small-scale information from a combination of gravitational shear and flexion. Including flexion allows us to supplement the shear on small scales in order to increase the sensitivity to substructures and the overall resolution of the convergence map without relying on strong lensing constraints. In order to preserve all available small scale information, we avoid any binning of the irregularly sampled input shear and flexion fields and treat the mass-mapping problem as a general ill-posed inverse problem, regularised us…
Metacalibration is a recently introduced method to accurately measure weak gravitational lensing shear using only the available imaging data, without need for prior information about galaxy properties or calibration from simulations. The method involves distorting the image with a small known shear, and calculating the response of a shear estimator to that applied shear. The method was shown to be accurate in moderate sized simulations with galaxy images that had relatively high signal-to-noise ratios, and without significant selection effects. In this work we introduce a formalism to correct …
We present weak lensing shear catalogues from the fourth data release of the Kilo-Degree Survey, KiDS-1000, spanning 1006 square degrees of deep and high-resolution imaging. Our `gold-sample' of galaxies, with well-calibrated photometric redshift distributions, consists of 21 million galaxies with an effective number density of $6.17$ galaxies per square arcminute. We quantify the accuracy of the spatial, temporal, and flux-dependent point-spread function (PSF) model, verifying that the model meets our requirements to induce less than a $0.1σ$ change in the inferred cosmic shear constraints on…
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 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…
Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of ray-tracing simulations with random realizations of spurious shear. This allows us to quantify the errors and biases of the triplet $(Ω_m,w,σ_8)$ derived from the power spectrum (PS), as well as from three different sets of non-Gaussian statistics of the lensing convergence field: Minkowski functionals (MF), low--order moments (LM), and peak counts (PK). Our main…
Upcoming surveys such as \LSST{} and \Euclid{} will significantly improve the power of weak lensing as a cosmological probe. To maximise the information that can be extracted from these surveys, it is important to explore novel statistics that complement standard weak lensing statistics such as the shear-shear correlation function and peak counts. In this work, we use a recently proposed weak lensing observable -- weak lensing voids -- to make parameter constraint forecasts for an LSST-like survey. We use the \cosmoslics{} $w$CDM simulation suite to measure void statistics as a function of cos…
We present the tomographic cross-correlation between galaxy lensing measured in the Kilo Degree Survey (KiDS-450) with overlapping lensing measurements of the cosmic microwave background (CMB), as detected by Planck 2015. We compare our joint probe measurement to the theoretical expectation for a flat $Λ$CDM cosmology, assuming the best-fitting cosmological parameters from the KiDS-450 cosmic shear and Planck CMB analyses. We find that our results are consistent within $1σ$ with the KiDS-450 cosmology, with an amplitude re-scaling parameter $A_{\rm KiDS} = 0.86 \pm 0.19$. Adopting a Planck cos…
