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 the measurement of the stellar velocity dispersion of the lensing galaxy, depends on the assumption that the ratio, $D_{\rm s}/D_{\rm ds}$, of angular diameter distances to the background quasar and between the lensing galaxy and the quasar can be constrained. This is typically achieved through the assumption of a particular cosmological model. Previous work (TDCOSMO IV) addressed the mass-sheet degeneracy and derived $H_{0}$ under the assumption of $Λ$CDM model. In this paper we show that the mass sheet degeneracy can be broken without relying on a specific cosmological model by combining lensing with relative distance indicators such as supernovae type Ia and baryon acoustic oscillations, which constrain the shape of the expansion history and hence $D_{\rm s}/D_{\rm ds}$. With this approach, we demonstrate that the mass-sheet degeneracy can be constrained in a cosmological-model-independent way, and hence model-independent distance measurements in time-delay cosmography under mass-sheet transformations can be obtained.
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 …
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 …
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…
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…
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）
To use strong gravitational lenses as an astrophysical or cosmological probe, models of their mass distributions are often needed. We present a new, time-efficient automation code for uniform modeling of strongly lensed quasars with GLEE, a lens modeling software, for high-resolution multi-band data. By using the observed positions of the lensed quasars and the spatially extended surface brightness distribution of the lensed quasar host galaxy, we obtain a model of the mass distribution of the lens galaxy. We apply this uniform modeling pipeline to a sample of nine strongly lensed quasars with…
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）
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…
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 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）
We make a number of comments regarding modeling degeneracies in strong lensing measurements of the Hubble parameter $H_0$. The first point concerns the impact of weak lensing associated with different segments of the line of sight. We show that external convergence terms associated with the lens-source and observer-lens segments need to be included in cosmographic modeling, in addition to the usual observer-source term, to avoid systematic bias in the inferred value of $H_0$. Specifically, we show how an incomplete account of some line of sight terms biases stellar kinematics as well as ray tr…
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 present extended modeling of the strong lens system RXJ1131-1231 with archival data in two HST bands in combination with existing line-of-sight contribution and velocity dispersion estimates. Our focus is on source size and its influence on time-delay cosmography. We therefore examine the impact of mass-sheet degeneracy and especially the degeneracy pointed out by Schneider & Sluse (2013) using the source reconstruction scale. We also extend on previous work by further exploring the effects of priors on the kinematics of the lens and the external convergence in the environment of the lensin…
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 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 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）
Time delay lensing is a mature and competitive cosmological probe. However, it is limited in accuracy by the well-known problem of the mass-sheet degeneracy: too rigid assumptions on the density profile of the lens can potentially bias the inference on cosmological parameters. I investigate the degeneracy between the choice of the lens density profile and the inference on the Hubble constant, focusing on double image systems. By expanding lensing observables in terms of the local derivatives of the lens potential around the Einstein radius, and assuming circular symmetry, I show that three deg…
Strongly gravitational lensed quasars can be used to measure the so-called time-delay distance $D_{Δt}$, and thus the Hubble constant $H_0$ and other cosmological parameters. Stellar kinematics of the deflector galaxy play an essential role in this measurement by: (i) helping break the mass-sheet degeneracy; (ii) determining in principle the angular diameter distance $D_{\rm d}$ to the deflector and thus further improving the cosmological constraints. In this paper we simulate observations of lensed quasars with integral field spectrographs and show that spatially resolved kinematics of the de…
Breaking the Mass-sheet Degeneracy in Time-delay Cosmology with Lensed and Unlensed Type Ia Supernovae
College of Physics, Hebei Normal University（河北师范大学物理学院）；Shijiazhuang Key Laboratory of Astronomy and Space Science, Hebei Normal University（河北师范大学石家庄天文与空间科学重点实验室）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）
Time delay measurements with Broken Power Law model
Institute for Frontier in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究所）；Shanghai Key Lab for Astrophysics, Shanghai Normal University（上海师范大学天体物理上海市重点实验室）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）
We study possible systematic effects on the values of the cosmological parameters measured through strong lensing analyses of the HFF galaxy cluster MACS J1149.5+2223. We use the observed positions of a large set of spectroscopically selected multiple images, including those of supernova "Refsdal" with their estimated time delays. Starting from our reference model in a flat $Λ$CDM cosmology, published in Grillo et al. (2018), we confirm the relevance of the longest measurable time delay, between SX and S1, and an approximately linear relation between its value and that of $H_{0}$. We perform t…
The central ambition of the modern time delay cosmography consists in determining the Hubble constant $H_0$ with a competitive precision. However, the tension with $H_0$ obtained from the Planck satellite for a spatially-flat $Λ$CDM cosmology suggests that systematic errors may have been underestimated. The most critical one probably comes from the degeneracy existing between lens models that was first formalized by the well-known mass-sheet transformation (MST). In this paper, we assess to what extent the source position transformation (SPT), a more general invariance transformation which con…
Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant ($H_0$) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: the lensed host galaxy can be observed before or after the transient's appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens mode…
The modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust modeling of the lens mass distribution. Unfortunately strong degeneracies between density profiles that lead to almost the same lensing observables may bias precise estimate for the Hubble constant. The source position transformation (SPT), which covers the well-known mass sheet transformation (MST) as a special case, defines a new framework to investigate these degeneracies. In this paper, we presen…
Investigating the Dark Energy Constraint from Strongly Lensed AGN at LSST-Scale
Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics, Stanford University（斯坦福大学卡弗里粒子天体物理与宇宙学研究所）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Institute for Particle Physics and Astrophysics, ETH Zurich（苏黎世联邦理工学院粒子物理与天体物理研究所）；Department of Astronomy, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校天文学系）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Department of Astronomy and Astrophysics, University of Chicago（芝加哥大学天文学与天体物理学系）；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）；Department of Physics and Astronomy, Stony Brook University（纽约州立大学石溪分校物理与天文学系）
