The subject of this paper is optimisation of weak lensing tomography: We carry out numerical minimisation of a measure of total statistical error as a function of the redshifts of the tomographic bin edges by means of a Nelder-Mead algorithm in order to optimise the sensitivity of weak lensing with respect to different optimisation targets. Working under the assumption of a Gaussian likelihood for the parameters of a $w_0 w_a$CDM-model and using Euclid's conservative survey specifications, we compare an equipopulated, equidistant and optimised bin setting and find that in general the equipopulated setting is very close to the optimal one, while an equidistant setting is far from optimal and also suffers from the ad hoc choice of a maximum redshift. More importantly, we find that nearly saturated information content can be gained using already few tomographic bins. This is crucial for photometric redshift surveys with large redshift errors. We consider a large range of targets for the optimisation process that can be computed from the parameter covariance (or equivalently, from the Fisher-matrix), extend these studies to information entropy measures such as the Kullback-Leibler-divergence and conclude that in many cases equipopulated binning yields results close to the optimum, which we support by analytical arguments.
CMB lensing tomography, or the cross-correlation between CMB lensing maps and large-scale structure tracers over a well-defined redshift range, has the potential to map the amplitude and growth of structure over cosmic time, provide some of the most stringent tests of gravity, and break important degeneracies between cosmological parameters. In this work, we use the unWISE galaxy catalog to provide three samples at median redshifts $z \sim 0.6, 1.1$ and 1.5, fully spanning the Dark Energy dominated era, together with the most recent Planck CMB lensing maps. We obtain a combined cross-correlati…
We describe a tomographic dissection of the Planck CMB lensing data, cross-correlating this map with galaxies in different ranges of photometric redshift. We use the nearly all-sky 2MPZ and WISExSCOS catalogues for z<0.35, extending to z<0.6 using SDSS. We describe checks for consistency between the different datasets, and perform a test for possible leakage of thermal Sunyaev--Zel'dovich signal into our cross-correlation measurements. The amplitude of the cross-correlation allows us to estimate the evolution of density fluctuations as a function of redshift, thus providing a test of theories …
We describe the first spectroscopic tomographic (spectrotomographic) weak lensing measurement for a galaxy cluster based only on background galaxies with spectroscopically determined redshifts. We use the massive cluster A2029 to demonstrate the power of combining spectroscopy and lensing to obtain accurate masses and to overcome biases from contamination and photometric redshift errors. We detect the shear signal from the cluster at $>3.9 σ$. The shear signal scales with source redshift in a way that is consistent with the angular diameter distance ratio variation in a $Λ$CDM Universe. Furthe…
We estimate uncertainties of cosmological parameters for phenomenological interacting dark energy models using weak lensing convergence power spectrum and bispectrum. We focus on the bispectrum tomography and examine how well the weak lensing bispectrum with tomography can constrain the interactions between dark sectors, as well as other cosmological parameters. Employing the Fisher matrix analysis, we forecast parameter uncertainties derived from weak lensing bispectra with a two-bin tomography and place upper bounds on strength of the interactions between the dark sectors. The cosmic shear w…
A number of recent, low-redshift, lensing measurements hint at a universe in which the amplitude of lensing is lower than that predicted from the $Λ$CDM model fit to the data of the Planck CMB mission. Here we use the auto- and cross-correlation signal of unWISE galaxies and Planck CMB lensing maps to infer cosmological parameters at low redshift. In particular, we consider three unWISE samples (denoted as "blue", "green" and "red") at median redshifts $z \sim 0.6$, $1.1$ and 1.5, which fully cover the Dark Energy dominated era. Our cross-correlation measurements, with combined significance $S…
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(Ω_m,w,σ_8)$ for an LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the …
We seek to clarify the origin of constraints on the dark energy equation of state parameter from CMB lensing tomography, that is the combination of galaxy clustering and the cross-correlation of galaxies with CMB lensing in a number of redshift bins. In particular, we consider the two-point correlation functions which can be formed with a catalog of galaxy locations and photometric redshifts from the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and CMB lensing maps from the CMB-S4 experiment. We focus on the analytic understanding of the origin of the constraints. Dark ener…
Recently, it has been shown that cross-correlating CMB lensing and 3D cosmic shear allows to considerably tighten cosmological parameter constraints. We investigate whether similar improvement can be achieved in a conventional tomographic setup. We present Fisher parameter forecasts for a Euclid-like galaxy survey in combination with different ongoing and forthcoming CMB experiments. In contrast to a fully three-dimensional analysis we find only marginal improvement. Assuming Planck-like CMB data we show that including the full covariance of the combined CMB and cosmic shear data improves the …
Optimising the sample selection for photometric galaxy surveys
Institute of Space Sciences (ICE, CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES（天文与行星学研究所，图卢兹大学）
We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg$^2$ of imaging data by the Kilo Degree Survey (KiDS) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of $N…
We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work with non-Gaussian posterior distributions which arise, for example, from a non-Gaussian prior distribution. In this work, we use a lognormal prior and compare the reconstruction results to a Gaussian prior in a suite of increasingly realistic tests on mock data. We find that in cases of high noise levels (i.e. for low source galaxy densities and/or high shape …
Combining weak lensing tomography and spectroscopic redshift surveys
红移空间畸变（RSD）是测量结构增长和检验广义相对论的有力手段，但它受到宇宙方差和星系偏差b与增长率因子f之间简并度的限制。透镜切变与星系密度场的互相关原则上可以不受宇宙方差限制地测量b，打破f-b简并，并允许从星系巡天中推断物质功率谱。我们分析的增长约束，从一个现实的层析弱透镜照片z调查结合光谱星系红移调查在同一天空区域。对于天空覆盖率f_sky=0.5，在z M_min=10^13 h^{-1}M_solar有光谱时，对横模的分析测量b到每个Δz=0.1仓2-3%的精度<1 when \sim 10 galaxies per square arcmin are measured in the lensing survey and all halos with M>。对于引力生长参数γ（f=Ω_m^γ），将透镜信息与非横模的RSD分析相结合，得出精度σ（γ）\sim 0.01。当光谱测量延伸到晕质量10^13.5（10^14）h^{-1} M_solar时，将透镜信息添加到RSD测量中可以使σ（γ）提高3倍（10倍）。我们还发现，重叠巡天的σ（γ）相当于1.5-2倍大的巡天的σ（γ），如果它们在天空上是分开的。当光谱质量阈值为10^13 - 10^14 h^{-1} M_solar时，这种增益最大，类似于LRG巡天。重叠勘测的增益对于非常深或非常浅的光谱勘测是减少的，但是任何实际…
Strong Lensing Tomography: Double and pseudo multi-source plane strong gravitational lensing to constrain dark energy
Stony Brook University（石溪大学）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Universidad Andres Bello（安德斯贝洛大学）；Oxford University（牛津大学）；University of Portsmouth（朴茨茅斯大学）
Multi-scale weak lensing detection of galaxy clusters with source redshift tomography
Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、法国原子能委员会、法国国家科学研究中心、天体物理学与分子天体物理学研究所）；Institute for Computational Cosmology, Department of Physics, Durham University（杜伦大学物理学院计算宇宙学研究所）；INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文空间科学观测站）；INFN – Sezione di Bologna（意大利国家核物理研究所博洛尼分部）；INAF – Istituto di Astrofisica Spaziale e Fisica cosmica di Milano（意大利国家天体物理研究所米兰空间天体物理与宇宙物理研究所）
Low-redshift constraints on structure growth from CMB lensing tomography
Università degli Studi di Trento（特伦托大学）；Università degli Studi di Torino（都灵大学）；INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino（意大利国家核物理研究所都灵分部）；University of Oxford（牛津大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）
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…
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…
Cosmic shear data contains a large amount of cosmological information encapsulated in the non-Gaussian features of the weak lensing mass maps. This information can be extracted using non-Gaussian statistics. We compare the constraining power in the $Ω_{\mathrm{m}} - σ_8$ plane of three map-based non-Gaussian statistics with the angular power spectrum, namely; peak/minimum counts and Minkowski functionals. We further analyze the impact of tomography and systematic effects originating from galaxy intrinsic alignments, multiplicative shear bias and photometric redshift systematics. We forecast th…
Cosmology from Planck CMB Lensing and DESI DR1 Quasar Tomography
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of California, Berkeley（加州大学伯克利分校）；University of Cambridge（剑桥大学）
In the context of next-generation spectroscopic galaxy surveys, new statistics of the distribution of matter are currently being developed. Among these, we investigated the angular redshift fluctuations (ARF), which probe the information contained in the projected redshift distribution of galaxies. Relying on the Fisher formalism, we show how ARF will provide complementary cosmological information compared to traditional angular galaxy clustering. We tested both the standard $\mathrm{ΛCDM}$ model and the $\mathrm{wCDM}$ extension. We find that the cosmological and galaxy bias parameters expres…
Massive cosmic neutrinos change the structure formation history by suppressing perturbations on small scales. Weak lensing data from galaxy surveys probe the structure evolution and thereby can be used to constrain the total mass of the three active neutrinos. However, much of the information is at small scales where the dynamics are nonlinear. Traditional approaches with second order statistics thus fail to fully extract the information in the lensing field. In this paper, we study constraints on the neutrino mass sum using lensing peak counts, a statistic which captures non-Gaussian informat…
We measure the cross-correlation between the galaxy density in the Dark Energy Survey (DES) Science Verification data and the lensing of the cosmic microwave background (CMB) as reconstructed with the Planck satellite and the South Pole Telescope (SPT). When using the DES main galaxy sample over the full redshift range $0.2 < z < 1.2$, a cross-correlation signal is detected at $6 σ$ and $4σ$ with SPT and Planck respectively. We then divide the DES galaxies into five photometric redshift bins, finding significant ($>$$2 σ$) detections in all bins. Comparing to the fiducial Planck cosmology, we …
To take full advantage of the unprecedented power of upcoming weak lensing surveys, understanding the noise, such as cosmic variance and geometry/mask effects, is as important as understanding the signal itself. Accurately quantifying the noise requires a large number of statistically independent mocks for a variety of cosmologies. This is impractical for weak lensing simulations, which are costly for simultaneous requirements of large box size (to cover a significant fraction of the past light cone) and high resolution (to robustly probe the small scale where most lensing signal resides). The…
Weak lensing peak counts are a powerful statistical tool for constraining cosmological parameters. So far, this method has been applied only to surveys with relatively small areas, up to several hundred square degrees. As future surveys will provide weak lensing datasets with size of thousands of square degrees, the demand on the theoretical prediction of the peak statistics will become heightened. In particular, large simulations of increased cosmological volume are required. In this work, we investigate the possibility of using simulations generated with the fast Comoving-Lagrangian accelera…
Gravitational waves from inspiraling compact objects provide us with information of the distance scale since we can infer the absolute luminosity of the source from analysis of the wave form, which is known as standard sirens. The first detection of the gravitational wave signal of the binary black hole merger event by Advanced LIGO has opened up the possibility of utilizing standard sirens as cosmological probe. In order to extract information of the distance-redshift relation, we cross-correlate weak lensing, which is an unbiased tracer of matter distribution in the Universe, with the projec…
Kinematic lensing (KL) is a new cosmological measurement technique that combines traditional weak lensing (WL) shape measurements of disc galaxies with their kinematic information. Using the Tully-Fisher relation KL breaks the degeneracy between intrinsic and observed ellipticity and significantly reduces the impact of multiple systematics that are present in traditional WL. We explore the performance of KL given the instrument capabilities of the $\textit{Roman Space Telescope}$, assuming overlap of the High Latitude Imaging Survey (HLIS), the High Latitude Spectroscopy Survey (HLSS) over 2,0…
The presence of massive neutrinos affects structure formation, leaving imprints on large-scale structure observables such as the weak lensing field. The common lensing analyses with two-point statistics are insensitive to the large amount of non-Gaussian information in the density field. We investigate non-Gaussian tools, in particular the Minkowski Functionals (MFs)---morphological descriptors including area, perimeter, and genus---in an attempt to recover the higher-order information. We use convergence maps from the Cosmological Massive Neutrino Simulations (\texttt{MassiveNus}) and assume …
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.…
We present a new method to measure the redshift-dependent galaxy bias by combining information from the galaxy density field and the weak lensing field. This method is based on Amara et al. (2012), where they use the galaxy density field to construct a bias-weighted convergence field kg. The main difference between Amara et al. (2012) and our new implementation is that here we present another way to measure galaxy bias using tomography instead of bias parameterizations. The correlation between kg and the true lensing field k allows us to measure galaxy bias using different zero-lag correlation…
