Strong lensing time delays can measure the Hubble constant H$_0$ independent of any other probe. Assuming commonly used forms for the radial mass density profile of the lenses, a 2\% precision has been achieved with 7 Time-Delay Cosmography (TDCOSMO) lenses, in tension with the H$_0$ from the cosmic microwave background. However, without assumptions on the radial mass density profile -- and relying exclusively on stellar kinematics to break the mass-sheet degeneracy -- the precision drops to 8\% with the current data of the 7 TDCOSMO lenses, insufficient to resolve the H$_0$ tension. With the addition of external information from 33 Sloan Lens ACS (SLACS) lenses, the precision improves to 5\%, {\it if} the deflectors of TDCOSMO and SLACS lenses are drawn from the same population. We investigate the prospects to improve the precision of time-delay cosmography without relying on mass profile assumptions to break the mass sheet degeneracy. Our forecasts are based on the hierarchical framework introduced by Birrer et al. (2020). With existing samples and technology, 3.3\% precision on H$_0$ can be reached by adding spatially resolved kinematics of the 7 TDCOSMO lenses. The precision improves to 2.5\% with the further addition of kinematics for 50 non-time-delay lenses from SLACS and the Strong Lensing Legacy Survey (SL2S). Expanding the samples to 40 time delay and 200 non-time delay lenses will improve the precision to 1.5\% and 1.2\%, respectively. Time-delay cosmography can reach sufficient precision to resolve the Hubble tension at 3-5$σ$, without assumptions on the radial mass profile of lens galaxies. By obtaining this precision with and without external datasets, we will test the consistency of the samples and enable further improvements based on even larger future samples of time delay and non-time-delay lenses (e.g. from the Rubin, Euclid, and Roman Observatories).
The H0LiCOW collaboration inferred via gravitational lensing time delays a Hubble constant $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{\rm Mpc}^{-1}$, describing deflector mass density profiles by either a power-law or stars plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in $H_0$. We quantify any potential effect of the MST with flexible mass models that are maximally degenerate with H0. Our calculation is based on a new hierarchical approach in which the MST is only constrained by …
Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant $H_0$. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer $H_0$. We base the mock lenses on six quadruply-imaged q…
In the context of gravitational lensing, the density profile of lensing galaxies is often considered to be perfectly elliptical. Potential angular structures are generally ignored, except to explain flux ratios anomalies. Surprisingly, the impact of azimuthal structures on extended images of the source has not been characterized, nor its impact on the H0 inference. We address this task by creating mock images of a point source embedded in an extended source, lensed by an elliptical galaxy on which multipolar components are added to emulate boxy/discy isodensity contours. Modeling such images w…
Time-delay cosmography with gravitationally lensed quasars plays an important role in anchoring the absolute distance scale and hence measuring the Hubble constant, $H_{0}$, independent of traditional distance ladder methodology. A current potential limitation of time delay distance measurements is the "mass-sheet transformation" (MST) which leaves the lensed imaging unchanged but changes the distance measurements and the derived value of $H_0$. In this work we show that the standard method of addressing the MST in time delay cosmography, through a combination of high-resolution imaging and th…
TDCOSMO. XXIII. Measurement of the Hubble constant from the doubly lensed quasar HE1104-1805
The University of Tokyo（东京大学）；Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Universitat de Barcelona (IEEC-UB)（巴塞罗那大学）；Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚高级研究学院）；UC Davis（加州大学戴维斯分校）；Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；ETH Zurich（苏黎世联邦理工学院）；Liège Université（列日大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Stony Brook University（石溪大学）；Fermi National Accelerator Laboratory（费米国家加速器实验室）
本文利用双镜像类星体HE1104-1805测量哈勃常数，通过结合多 telescope 数据测量时间延迟、恒星速度弥散、费马势差和收敛，采用幂律质量模型得出H_0=64.2±5.8xλ_int km s⁻¹ Mpc⁻¹。
We have measured the redshifts and single-aperture velocity dispersions of eight lens galaxies using the data collected by the Echellette Spectrograph and Imager (ESI) and Low Resolution Imaging Spectrometer (LRIS) at W.M. Keck observatory on different observing nights spread over three years (2018-2020). These results, combined with other ancillary data, such as high-resolution images of the lens systems, and time delays, are necessary to increase the sample size of the quasar-galaxy lens systems for which the Hubble constant can be measured, using the time-delay strong lensing method, hence …
TDCOSMO 2026: new insights on the Hubble tension from strong lensing time delays
Stony Brook University（石溪大学）；University of Oxford（牛津大学）；Universitat de Barcelona（巴塞罗那大学）；Institut Català de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高级研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；University of California, Davis（加州大学戴维斯分校）；Université de Montpellier（蒙彼利埃大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；University of Geneva（日内瓦大学）
TDCOSMO 2026: A 3% measurement of the Hubble constant from strong lensing and stellar kinematics
Stony Brook University（石溪大学）；University of Oxford（牛津大学）；Universitat de Barcelona（巴塞罗那大学）；Institut Català de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高级研究院）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究研究所）；University of California, Davis（加州大学戴维斯分校）；Université de Montpellier（蒙彼利埃大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；University of Geneva（日内瓦大学）
TDCOSMO 2025: Cosmological constraints from strong lensing time delays
Stony Brook University（石溪大学）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；University of Chicago（芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙学物理研究所）；SLAC National Laboratory（斯坦福直线加速器中心）；University of Oxford（牛津大学）；Universitat de Barcelona（巴塞罗那大学）；Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚高级研究学院）；European Southern Observatory（欧洲南方天文台）；Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；UC Davis（加州大学戴维斯分校）
TDCOSMO 2025利用强引力透镜时间延迟数据，结合超新星数据，得出H₀=71.6±3.9 km s⁻¹ Mpc⁻¹的宇宙学约束，并在多种宇宙学模型中保持一致性。
TDCOSMO XXV: Measuring H0 to 6.5% precision with quasar strong lensing and maximally flexible mass-sheet dynamics
University of California, Los Angeles（加州大学洛杉矶分校）；ETH Zurich（苏黎世联邦理工学院）；Université de Genève（日内瓦大学）；European Southern Observatory（欧洲南方天文台）；Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Stony Brook University（石溪大学）；Université de Montpellier（蒙彼利埃大学）
基于四重成像类星体SDSSJ1433+6007，结合哈勃空间望远镜成像、时间延迟监测和空间分辨恒星运动学，通过联合透镜和动力学模型并考虑质量片变换的最大灵活性，在平坦ΛCDM宇宙学下以6.5%精度测得哈勃常数$H_0 = 73.2^{+4.8}_{-4.7}$ km s$^{-1}$ Mpc$^{-1}$，并发现内部质量片参数$λ_{\rm int}=1.12^{+0.05}_{-0.06}$与1有2σ偏离。
TDCOSMO XXVIII. The Hubble constant from the quadruply lensed quasar J1537$-$3010 with precise time delays
University of Geneva（日内瓦大学）；Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；Laboratoire Univers et Particules de Montpellier (LUPM), CNRS & Université Montpellier（蒙彼利埃宇宙与粒子实验室（LUPM），法国国家科学研究中心与蒙彼利埃大学）；STAR Institute, University of Liège（列日大学STAR研究所）；Armagh Observatory and Planetarium（阿马天文台和天文馆）；Fermi National Accelerator Laboratory（费米国家加速器实验室）
TDCOSMO XXIV. First spatially resolved kinematics of the lens galaxy obtained using JWST-NIRSpec to improve time-delay cosmography
Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Center for Astronomy, Space Science and Astrophysics, Independent University, Bangladesh（孟加拉独立大学天文学、空间科学与天体物理中心）；Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理与天文系）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学自然科学院物理系）；Max Planck Institute for Astrophysics（马克斯·普朗克天体物理学研究所）；Space Telescope Science Institute（太空望远镜科学研究所）；Sub-Department of Astrophysics, Department of Physics, University of Oxford（牛津大学物理系天体物理子部门）
TDCOSMO XXIX: JWST/NIRSpec IFU Spatially Resolved Kinematics of Three Time-delay Lenses
University of California, Los Angeles（加州大学洛杉矶分校）；University of Chicago（芝加哥大学）；Independent University, Bangladesh（孟加拉独立大学）；University of Oxford（牛津大学）；Space Telescope Science Institute（太空望远镜科学研究所）；Stony Brook University（石溪大学）；Tohoku University（东北大学）
The importance of alternative methods for measuring the Hubble constant, such as time-delay cosmography, is highlighted by the recent Hubble tension. It is paramount to thoroughly investigate and rule out systematic biases in all measurement methods before we can accept new physics as the source of this tension. In this study, we perform a check for systematic biases in the lens modelling procedure of time-delay cosmography by comparing independent and blind time-delay predictions of the system WGD 2038-4008 from two teams using two different software programs: GLEE and LENSTRONOMY. The predic…
Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble constant, $H_0$. As part of an ongoing effort to uncover and control systematic uncertainties, we investigate three potential sources: 1- stellar kinematics, 2- line-of-sight effects, and 3- the deflector mass model. To meet this goal in a quantitative way, we reproduced the H0LiCOW/SHARP/STRIDES (hereafter TDCOSMO) procedures on a set of real and simulated data, and we find the following. First, stellar kinematics cannot be a dominant source of error or bias since we find that a systematic ch…
The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H_0$. A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated on a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as…
TDCOSMO XIX. Measuring stellar velocity dispersion with sub-percent accuracy for cosmography
University of California, Los Angeles（加州大学洛杉矶分校）；University of Chicago（芝加哥大学）；Independent University, Bangladesh（孟加拉国独立大学）；University of Oxford（牛津大学）；Stony Brook University（石溪大学）
TDCOSMO: XX. WFI2033--4723, the First Quadruply-Imaged Quasar Modeled with JWST Imaging
Department of Physics and Astronomy, UCLA（加州大学洛杉矶分校物理与天文系）；Department of Physics and Astronomy, Stony Brook University（纽约州立大学石溪分校物理与天文系）；Department of Astronomy and Astrophysics, University of Chicago（芝加哥大学天文与天体物理系）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Center for Astronomy, Space Science and Astrophysics, Independent University, Bangladesh（孟加拉国独立大学天文学、空间科学与天体物理中心）；Research Center for the Early Universe, Graduate School of Science, The University of Tokyo（东京大学理学研究科早期宇宙研究中心）；IPAC, California Institute of Technology（加州理工学院红外处理分析中心）；Space Telescope Science Institute（太空望远镜科学研究所）
TDCOSMO XXVI: Uniform lens modeling of eight doubly imaged quasars
Stony Brook University（石溪大学）；University of Chicago（芝加哥大学）；Independent University, Bangladesh（孟加拉独立大学）；Stockholm University（斯德哥尔摩大学）；ETH Zurich（苏黎世联邦理工学院）；Université de Genève（日内瓦大学）；Universidad de Valparaíso（瓦尔帕莱索大学）；University of Liège（列日大学）；Universitat de Barcelona（巴塞罗那大学）；Institut Català de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚高级研究所）；Institut dEstudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究研究所）
TDCOSMO XXXI: New techniques in line-of-sight studies of time delay lenses
CNRS & Université de Montpellier（法国国家科学研究中心与蒙彼利埃大学）；University of California, Los Angeles（加州大学洛杉矶分校）；University of California, Davis（加州大学戴维斯分校）；Argonne National Laboratory（阿贡国家实验室）；Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Université de Genève（日内瓦大学）
TDCOSMO XIV: Practical Techniques for Estimating External Convergence of Strong Gravitational Lens Systems and Applications to the SDSS J0924+0219 System
We use supernovae measurements, calibrated by the local determination of the Hubble constant $H_0$ by SH0ES, to interpolate the distance-redshift relation using Gaussian process regression. We then predict, independent of the cosmological model, the distances that are measured with strong lensing time delays. We find excellent agreement between these predictions and the measurements. The agreement holds when we consider only the redshift dependence of the distance-redshift relation, independent of the value of $H_0$. Our results disfavor the possibility that lens mass modeling contributes a 10…
TDCOSMO. XXVII. JWST-based Lens Models and H$_0$ Measurement of WFI2033, HE0435, and PG1115
University of California, Los Angeles（加州大学洛杉矶分校）；CNRS & Université Montpellier（法国国家科学研究中心与蒙彼利埃大学）；Stony Brook University（纽约州立大学石溪分校）；UC Davis（加州大学戴维斯分校）；University of Geneva（日内瓦大学）；University of Chicago（芝加哥大学）；Independent University, Bangladesh（孟加拉独立大学）；The University of Tokyo（东京大学）
Strong gravitational lensing has been a powerful probe of cosmological models and gravity. To date, constraints in either domain have been obtained separately. We propose a new methodology through which the cosmological model, specifically the Hubble constant, and post-Newtonian parameter can be simultaneously constrained. Using the time-delay cosmography from strong lensing combined with the stellar kinematics of the deflector lens, we demonstrate the Hubble constant and post-Newtonian parameter are incorporated in two distance ratios which reflect the lensing mass and dynamical mass, respect…
We investigate the origin of $Λ$CDM parameter constraints in weak lensing, with a focus on the Hubble constant. We explain why current cosmic shear data are sensitive to the parameter combination $S_8 \propto σ_8 Ω_m^{0.5}$, improving upon previous studies through use of the halo model. Motivated by the ongoing discrepancy in measurements of the Hubble constant from high and low redshift, we explain why cosmic shear provides almost no constraint on $H_0$ by showing how the lensing angular power spectrum depends on physical length scales in the dark matter distribution. We derive parameter cons…
We study shapes and alignments of 45 dark matter (DM) haloes and their brightest cluster galaxies (BCGs) using a sample of 39 massive clusters from Hubble Frontier Field (HFF), Cluster Lensing And Supernova survey with Hubble (CLASH), and Reionization Lensing Cluster Survey (RELICS). We measure shapes of the DM haloes by strong gravitational lensing, whereas BCG shapes are derived from their light profiles in Hubble Space Telescope images. Our measurements from a large sample of massive clusters presented here provide new constraints on dark matter and cluster astrophysics. We find that DM hal…
Hubble Frontier Fields : A High-Precision Strong-Lensing Mass Model of the Massive Galaxy Cluster Abell 2744 using 180 Multiple Images
我们提出了一个高精度的星系团阿贝尔2744的质量模型，强引力透镜分析的基础上的\emph{Hubble Space Telescope Frontier Fields}（HFF）的成像数据，现在包括两个\emph{Advanced Camera for Surveys}和\emph{Wide-Field Camera 3}观测到的最终深度。利用可见光和近红外数据前所未有的深度，我们确定了34个新的多重成像星系，使总数达到61个，包括181个单独的透镜图像。在这个过程中，我们纠正以前的错误识别和位置的集群核心的北部的多个系统。使用\textsc{Lenstool}软件和新的多组图像，我们使用两个星系团规模的暗物质晕和星系团成员的星系团规模的晕来模拟星系团。我们的最佳拟合模型预测图像的位置与\emph{RMS}的误差为0.69 $\arcsec$，这构成了一个改进的几乎是一个因素的两个在以前的参数模型，这个集群。我们测量了200 kpc口径内的总投影质量（$2.162\pm 0.005$）$\times 10^{14}M_{\odot}$，从而继最近的HFF测量MACSJ 0416.1 -2403之后，第二次达到1级精度。重要的是，质量模型的更高质量转化为导出的放大因子的4倍的总体改进。%的高红移透镜背景星系。与我们以前的HFF引力透镜分析一起，这项工作表明，HFF数据能够对大质量星系…
The presence of mass inhomogeneities along the line of sight of propagation of light fromdistant objects can induce deflection in the flight path of the photon. This phenomenon is called as gravitational lensing. Lensing can have both distortion (shear) and isotropic magnification effects on the source. We studied the effect of lensing magnification on supernova (SN) Ia in this thesis. Presence of lensing would introduce a source of contamination to the brightness distribution of the source (SN Ia in our case). Thus it also enables one to compute the lensing effect indirectly from the Hubble d…
Cluster lensing has become an important tool in the search for high redshift galaxies through its ability to magnify sources. In order to determine the intrinsic properties of these galaxies, lensing mass models must be constructed to determine the magnification of the images. These models are traditionally two-dimensional, focusing on the mass within the cluster and either ignoring or approximating any contribution from line-of-sight galaxies. In this paper, we present the first full set of three-dimensional mass models of the six Hubble Frontier Fields and use them to test for systematic bia…
Measurements of the Hubble constant, $H_0$, from the cosmic distance ladder are currently in tension with the value inferred from Planck observations of the CMB and other high redshift datasets if a flat $Λ$CDM cosmological model is assumed. One of the few promising theoretical resolutions of this tension is to invoke new physics that changes the sound horizon scale in the early universe; this can bring CMB and BAO constraints on $H_0$ into better agreement with local measurements. In this paper, we discuss how a measurement of the Hubble constant can be made from the CMB without using informa…
The stellar velocity anisotropy of strong lensing massive elliptical galaxies and its role in the inference of the Hubble parameter $H_0$ using spatially resolved kinematics
American Museum of Natural History（美国自然历史博物馆）；The Graduate Center of the City University of New York（纽约市立大学研究生中心）；Lehman College of the CUNY（纽约市立大学雷曼学院）；Borough of Manhattan Community College, City University of New York（纽约市立大学曼哈顿社区学院）
For a flat $Λ$CDM (standard) cosmology, a small sample of gravitationally lensed quasars with measured time delays has recently provided a value of the Hubble constant $H_0$ in tension with the $Planck$ flat $Λ$CDM result. Trying to check if this tension is real or not, we used basic observational constraints for two double quasars of the GLENDAMA sample (SBS 0909+532 and SDSS J1339+1310) to discuss the underlying value of $H_0$ in a standard cosmology. For SBS 0909+532, we were not able to obtain a reliable measurement of $H_0$. However, the current data of SDSS J1339+1310 are consistent with…
Constraints on a $ϕ$CDM model from strong gravitational lensing and updated Hubble parameter measurements
我们用逆幂律势约束标量场暗能量模型，即，$V(ϕ)\propto ϕ^{-α}$（$α>0$），从一组最近的宇宙学观测，通过汇编更新的样本哈勃参数测量，包括30个独立的数据点。我们的结果表明，更新后的样本的$H(z)$数据与HST先验的$H_0$的约束力强于SCP Union2和Union2.1编译。最近的一个强引力透镜系统的样本也被用来限制模型，即使结果并不显著。通过对强引力透镜数据与更严格的更新哈勃参数测量和SCP Union 2的Ia型超新星数据的联合分析表明，目前的观测仍然不能区分暗能量是一个与时间无关的宇宙学常数还是一个随时间变化的动力学分量。
We present free-form gravitational lensing models derived with the WSLAP+ code for the six $\textit{Hubble Frontier Fields}$ clusters using the latest data available from the $\textit{Frontier Fields Lensing Models v.4}$ collaboration. We present magnifications maps in the lens plane and caustic maps in the source plane. From these maps, we derive the probability of magnification using two different, but related, methods. We confirm MACS 0717 as the cluster with the most complex structure, and having the largest lensing efficiency and Einstein radius. When comparing these results with the ones…
