上下文引力透镜是了解宇宙黑暗面的主要工具之一。准确，高效和有效的方法，能够提取这些信息以及其他宇宙学参数从宇宙剪切数据的需求正在不断增长。COSEBIs（Complete Orthogonal Sets of E-/B-Integrals）是最近发展起来的一种统计测度，它包含了在有限角度范围内测量的剪切关联函数中包含的完整的E-/B-模式可分离信息。目标。本工作的目的是测试这个新开发的统计高维参数空间的属性，并推广和测试剪切层析成像。方法.我们使用Fisher分析来研究COSEBI的有效性。我们展示了我们的结果的品质因数的数量，基于Fisher矩阵。结果我们发现，一个相对较小的COSEBI模式的数量总是足以饱和到最大的信息水平。这个数字总是小于“对数COSEBI”比“线性COSEBI”，也取决于红移箱的数量，宇宙学参数的数量和选择，以及调查的特点。结论. COSEBI提供了一种非常紧凑的分析宇宙剪切数据的方法，即，将数据中所有E/B模式可分离的二阶统计信息约简为少量COSEBI模式。此外，使用该方法，数据分箱中的任意性不再是问题，因为COSEBI模式是离散的。最后，少量的模式也意味着协方差及其倒数更容易获得，例如，从数值模拟，比剪切关联函数本身。
英文摘要：
Context. Gravitational lensing is one of the leading tools in understanding the dark side of the Universe. The need for accurate, efficient and effective methods which are able to extract this information along with other cosmological parameters from cosmic shear data is ever growing. COSEBIs, Complete Orthogonal Sets of E-/B-Integrals, is a recently developed statistical measure that encompasses the complete E-/B-mode separable information contained in the shear correlation functions measured on a finite angular range. Aims. The aim of the present work is to test the properties of this newly developed statistics for a higher-dimensional parameter space and to generalize and test it for shear tomography. Methods. We use Fisher analysis to study the effectiveness of COSEBIs. We show our results in terms of figure-of-merit quantities, based on Fisher matrices. Results. We find that a relatively small number of COSEBIs modes is always enough to saturate to the maximum information level. This number is always smaller for 'logarithmic COSEBIs' than for 'linear COSEBIs', and also depends on the number of redshift bins, the number and choice of cosmological parameters, as well as the survey characteristics. Conclusions. COSEBIs provide a very compact way of analyzing cosmic shear data, i.e., all the E-/B-mode separable second-order statistical information in the data is reduced to a small number of COSEBIs modes. Furthermore, with this method the arbitrariness in data binning is no longer an issue since the COSEBIs modes are discrete. Finally, the small number of modes also implies that covariances, and their inverse, are much more conveniently obtainable, e.g., from numerical simulations, than for the shear correlation functions themselves.
We perform a cosmic shear analysis of HSC survey first-year data (HSC-Y1) using Complete Orthogonal Sets of E/B-Integrals (COSEBIs) to derive cosmological constraints. We compute E/B-mode COSEBIs from cosmic shear two-point correlation functions measured on an angular range of $4\arcmin<θ<180\arcmin$. We perform the standard Bayesian likelihood analysis for cosmological inference from the measured E-mode COSEBIs, including contributions from intrinsic alignments of galaxies as well as systematic effects from point spread function model errors, shear calibration uncertainties, and source redshi…
We present cosmological constraints from a joint cosmic shear analysis of the Kilo-Degree Survey (KV450) and the Dark Energy Survey (DES-Y1), conducted using Complete Orthogonal Sets of E/B-Integrals (COSEBIs). With COSEBIs we isolate any B-modes which have a non-cosmic shear origin and demonstrate the robustness of our cosmological E-mode analysis as no significant B-modes are detected. We highlight how COSEBIs are fairly insensitive to the amplitude of the non-linear matter power spectrum at high $k$-scales, mitigating the uncertain impact of baryon feedback in our analysis. COSEBIs, therefo…
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 METACALIBRATION shear catalogue. This is in contrast to the secondary IM3SHAPE shear catalogue, where we detect B- modes at a significance of $\sim 3σ$ 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 …
One probe for systematic effects in gravitational lensing surveys is the presence of so-called B-modes in the cosmic shear two-point correlation functions ξ_\pm(\vt), since lensing is expected to produce only E-mode shear. Furthermore, there exist ambiguous modes which can not uniquely be assigned to either E- or B-mode shear. We derive explicit equations for the pure-mode shear correlation functions ξ_\pm^E/B(\vt) and their ambiguous components ξ_\pm^amb(\vt), that can be derived from the measured ξ_\pm(\vt) on a finite angular interval \tmin\le\vt\le\tmax, such that the latter can be decompo…
KiDS-Legacy: Joint analysis of second- and third-order cosmic shear
Universität Innsbruck（因斯布鲁克大学）；Universität Bonn（波恩大学）；University of Waterloo（滑铁卢大学）；Newcastle University（纽卡斯尔大学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；Polish Academy of Sciences（波兰科学院）；Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology（巴塞罗那高等物理研究所，巴塞罗那科学与技术学院）；University of Edinburgh（爱丁堡大学）；Ruhr University Bochum（鲁尔大学波鸿）；Leiden University（莱顿大学）
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 cosmic shear analysis with an improved redshift calibration for the fourth data release of the Kilo-Degree Survey (KiDS-1000) using self-organising maps (SOMs). Compared to the previous analysis of the KiDS-1000 data, we expand the redshift calibration sample to more than twice its size, now consisting of data of 17 spectroscopic redshift campaigns, and significantly extending the fraction of KiDS galaxies we are able to calibrate with our SOM redshift methodology. We then enhance the calibration sample with precision photometric redshifts from COSMOS2015 and the Physics of the Ac…
We performed an internal-consistency test of the KiDS+VIKING-450 (KV450) cosmic shear analysis with a colour-based split of source galaxies. Utilising the same measurements and calibrations for both sub-samples, we inspected the characteristics of the shear measurements and the performance of the calibration pipelines. On the modelling side, we examined the observational nuisance parameters, specifically those for the redshift calibration and intrinsic alignments, using a Bayesian analysis with dedicated test parameters. We verified that the current nuisance parameters are sufficient for the K…
We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), doubling the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat $Λ$CDM model, we find $S_8 = σ_8 (Ω_{\rm m}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021}$ for our fiducial analysis, which is in $3σ$ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary an…
UNIONS is an ongoing collaboration that will provide the largest deep photometric survey of the Northern sky in four optical bands to date. As part of this collaboration, CFIS is taking $r$-band data with an average seeing of 0.65 arcsec, which is complete to magnitude 24.5 and thus ideal for weak-lensing studies. We perform the first weak-lensing analysis of CFIS $r$-band data over an area spanning 1700 deg$^2$ of the sky. We create a catalogue with measured shapes for 40 million galaxies, corresponding to an effective density of 6.8 galaxies per square arcminute, and demonstrate a low level …
We present a tomographic cosmic shear analysis of the Kilo-Degree Survey (KiDS) combined with the VISTA Kilo-Degree Infrared Galaxy Survey (VIKING). This is the first time that a full optical to near-infrared data set has been used for a wide-field cosmological weak lensing experiment. This unprecedented data, spanning $450~$deg$^2$, allows us to improve significantly the estimation of photometric redshifts, such that we are able to include robustly higher-redshift sources for the lensing measurement, and - most importantly - solidify our knowledge of the redshift distributions of the sources.…
Minkowski functionals (MFs) quantify the topological properties of a given field probing its departure from Gaussianity. We investigate their use on lensing convergence maps in order to see whether they can provide further insights on the underlying cosmology with respect to the standard second-order statistics, i.e., cosmic shear tomography. To this end, we first present a method to match theoretical predictions with measured MFs taking care of the shape noise, imperfections in the map reconstruction, and inaccurate description of the nonlinearities in the matter power spectrum and bispectrum…
We investigate the feasibility of extracting Baryon Acoustic Oscillations (BAO) from cosmic shear tomography. We particularly focus on the BAO scale precision that can be achieved by future spectroscopy-based, kinematic weak lensing (KWL) surveys \citep[e.g.,][]{Huff13} in comparison to the traditional photometry-based weak lensing surveys. We simulate cosmic shear tomography data of such surveys with a few simple assumptions to focus on the BAO information, extract the spacial power spectrum, and constrain the recovered BAO feature. Due to the small shape noise and the shape of the lensing ke…
Probing the Cosmological Principle with CMB lensing and cosmic shear
University of the Western Cape（西开普敦大学）；National Institute for Theoretical & Computational Sciences（理论与计算科学国家研究所）；Laboratoire Univers et Particules de Montpellier, CNRS & Université de Montpellier（蒙彼利埃宇宙与粒子实验室，法国国家科学研究中心与蒙彼利埃大学）；Queen Mary University of London（伦敦玛丽女王大学）；Université de Genève（日内瓦大学）
We present a tomographic weak lensing analysis of the Kilo Degree Survey Data Release 4 (KiDS-1000), using a new pseudo angular power spectrum estimator (pseudo-$C_{\ell}$) under development for the ESA Euclid mission. Over 21 million galaxies with shape information are divided into five tomographic redshift bins, ranging from 0.1 to 1.2 in photometric redshift. We measured pseudo-$C_{\ell}$ using eight bands in the multipole range $76<\ell<1500$ for auto- and cross-power spectra between the tomographic bins. A series of tests were carried out to check for systematic contamination from a varie…
We describe a new method for reducing the shape noise in weak lensing measurements by an order of magnitude. Our method relies on spectroscopic measurements of disk galaxy rotation and makes use of the Tully-Fisher relation in order to control for the intrinsic orientations of galaxy disks. For this new proposed method, so-called Kinematic Lensing (KL), the shape noise ceases to be an important source of statistical error. We use the CosmoLike software package to simulate likelihood analyses for two Kinematic Lensing survey concepts (roughly similar in scale to Dark Energy Survey Task Force St…
Upcoming deep imaging surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time will be confronted with challenges that come with increased depth. One of the leading systematic errors in deep surveys is the blending of objects due to higher surface density in the more crowded images; a considerable fraction of the galaxies which we hope to use for cosmology analyses will overlap each other on the observed sky. In order to investigate these challenges, we emulate blending in a mock catalogue consisting of galaxies at a depth equivalent to 1.3 yr of the full 10-yr Rubin Obser…
Upcoming photometric lensing surveys will considerably tighten constraints on the neutrino mass and the dark energy equation of state. Nevertheless it remains an open question of how to optimally extract the information and how well the matter power spectrum must be known to obtain unbiased cosmological parameter estimates. By performing a Principal Component Analysis (PCA), we quantify the sensitivity of 3D cosmic shear and tomography with different binning strategies to different regions of the lensing kernel and matter power spectrum, and hence the background geometry and growth of structur…
Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological param…
Cosmic Shear Measurements with DES Science Verification Data
我们目前的测量弱引力透镜宇宙剪切两点统计使用暗能量调查科学验证数据。我们证明了我们的结果对剪切测量管道的选择是鲁棒的，无论是ngmix还是im3shape，并且对两点统计量的选择是鲁棒的，包括实数和傅立叶空间统计量。我们的结果通过了一套零测试，包括测试B模式污染和直接测试的任何依赖的两点函数上的一组16个观测条件和星系的属性，如看到，空气质量，星系的颜色，星系的大小等，我们还使用了一个大的模拟套件来计算宇宙剪切测量的协方差矩阵，并分配统计意义，我们的零测试。我们发现我们的协方差矩阵与晕轮模型预测一致，表明它具有适当水平的晕轮样本方差。我们比较了相同的刀切程序应用于数据和模拟，以寻找其他来源的噪声没有捕捉到的模拟。我们在数据中没有发现统计上显著的额外噪声源。对于我们的最高源密度目录，断层扫描的总体检测显著性为9.7sigma。这项工作中测量的宇宙学约束在一篇配套论文中提出（DES et al. 2015）。
The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on the accurate knowledge of the galaxy mean redshift $\langle z \rangle$. We investigate the possibility of measuring $\langle z \rangle$ with an accuracy better than $0.002\,(1+z)$, in ten tomographic bins spanning the redshift interval $0.2<z<2.2$, the requirements for the cosmic shear analysis of Euclid. We implement a sufficiently realistic simulation to understand the advantages, compleme…
