Measurements of time-delay cosmography of lensed quasars can provide an independent probe to explore the expansion history of the late-time Universe. In this paper, we employ the time-delay cosmography measurements from seven lenses (here abbreviated as the TD data) to constrain interacting dark energy (IDE) models. We mainly focus on the scenario of vacuum energy (with $w=-1$) interacting with cold dark matter, and consider four typical cases of the interaction form $Q$. When the TD data alone are employed, we find that the IDE models with $Q\propto ρ_{\rm de}$ seem to have an advantage in relieving the $H_{0}$ tension between the cosmic microwave background (CMB) and TD data. When the TD data are added to the CMB$+$BAO$+$SN$+H_0$ data, we find that: (i) the coupling parameter $β$ in all the considered IDE models is positive within 1$σ$ range, implying a mild preference for the case of cold dark matter decaying into dark energy; (ii) the IDE model with $Q = βH_{0} ρ_{\rm c}$ slightly relieves the $S_8$ tension, but the other considered IDE models further aggravate this tension; (iii) the Akaike information criteria of the IDE models with $Q \propto ρ_{\rm c}$ are lower than that of the $Λ$CDM model, indicating that these IDE models are more preferred by the current mainstream data. We conclude that the considered IDE models have their own different advantages when the TD data are employed, and none of them can achieve good scores in all aspects.
Strong lensing cosmography using binary-black-hole mergers: Prospects for the near future
International Centre for Theoretical Science, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；Department of Physics, The Chinese University of Hong Kong（香港中文大学物理系）；Department of Physics, University of California at Santa Barbara（加州大学圣塔芭芭拉分校物理系）
LISA might detect gravitational waves from mergers of massive black hole binaries strongly lensed by intervening galaxies (Sereno et al. 2010). The detection of multiple gravitational lensing events would provide a new tool for cosmography. Constraints on cosmological parameters could be placed by exploiting either lensing statistics of strongly lensed sources or time delay measurements of lensed gravitational wave signals. These lensing methods do not need the measurement of the redshifts of the sources and the identification of their electromagnetic counterparts. They would extend cosmologic…
It has recently been proposed that gravitationally lensed type-Ia supernovae can provide microlensing-free time-delay measurements provided that the measurement is taken during the achromatic expansion phase of the explosion and that color light curves are used rather than single-band light curves. If verified, this would provide both precise and accurate time-delay measurements, making lensed type-Ia supernovae a new golden standard for time-delay cosmography. However, the 3D geometry of the expanding shell can introduce an additional bias that has not yet been fully explored. In this work, w…
Forecasting Constraints on Cosmology and Modified Gravitational-wave Propagation by Combining Strongly Lensed Gravitational Waves and Galaxy Surveys
International Center for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（国际理论物理中心亚太分部，中国科学院大学）；Taiji Laboratory for Gravitational Wave Universe, University of Chinese Academy of Sciences（太极引力波宇宙实验室，中国科学院大学）
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…
We present a measurement of the Hubble constant ($H_{0}$) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat $Λ$CDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement, in agreement with local measurements of $H_{0}$ from type Ia supernovae calibrated by the distance ladder, but in $3.1σ$ tension with $Planck$ observations of the cosmic microwave background (CMB). This method is completely indepen…
Follow-up of SN 2025wny V: Lens Modelling and Cosmography of a Strongly Lensed Superluminous Supernova at $z = 2.015$ using Space Data
Stockholm University（斯德哥尔摩大学）；University of Birmingham（伯明翰大学）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Portsmouth（朴茨茅斯大学）；University of Cambridge（剑桥大学）
Gravitational time delays, observed in strong lens systems where the variable background source is multiply-imaged by a massive galaxy in the foreground, provide direct measurements of cosmological distance that are very complementary to other cosmographic probes. The success of the technique depends on the availability and size of a suitable sample of lensed quasars or supernovae, precise measurements of the time delays, accurate modeling of the gravitational potential of the main deflector, and our ability to characterize the distribution of mass along the line of sight to the source. We rev…
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…
Astrometric precision and knowledge of the point spread function are key ingredients for a wide range of astrophysical studies including time-delay cosmography in which strongly lensed quasar systems are used to determine the Hubble constant and other cosmological parameters. Astrometric uncertainty on the positions of the multiply-imaged point sources contributes to the overall uncertainty in inferred distances and therefore the Hubble constant. Similarly, knowledge of the wings of the points spread function (PSF) is necessary to disentangle light from the background sources and the foregroun…
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…
One of the primary mission objectives for the Roman Space Telescope is to investigate the nature of dark energy with a variety of methods. Observations of Type Ia supernovae (SNIa) will be one of the principal anchors of the Roman cosmology program, through traditional luminosity distance measurements. This SNIa cosmology program can provide another valuable cosmological probe, without altering the mission strategy: time delay cosmography with gravitationally lensed SN. In this work, we forecast lensed SN cosmology constraints with the Roman Space Telescope, while providing useful tools for fu…
The upcoming Large Synoptic Survey Telescope (LSST) will detect many strongly lensed Type Ia supernovae (LSNe Ia) for time-delay cosmography. This will provide an independent and direct way for measuring the Hubble constant $H_0$, which is necessary to address the current $4.4 σ$ tension in $H_0$ between the local distance ladder and the early Universe measurements. We present a detailed analysis of different observing strategies for the LSST, and quantify their impact on time-delay measurement between multiple images of LSNe Ia. For this, we produced microlensed mock-LSST light curves for whi…
We explore the use of strong lensing by galaxy clusters to constrain the dark energy equation of state and its possible time variation. The cores of massive clusters often contain several multiply imaged systems of background galaxies at different redshifts. The locations of lensed images can be used to constrain cosmological parameters due to their dependence on the ratio of angular diameter distances. We employ Monte-Carlo simulations of cluster lenses, including the contribution from substructures, to assess the feasibility of this potentially powerful technique. At the present, parametric …
We present a novel, purely geometric probe of cosmology based on measurements of differential time delays between images of strongly lensed quasars due to finite source effects. Our approach is solely dependent on cosmology via a ratio of angular diameter distances, the image separation, and the source size. It thereby entirely avoids the challenges of lens modelling that conventionally limit time delay cosmography, and instead entails the lensed reverberation mapping of the quasar Broad Line Region. We demonstrate that differential time delays are measurable with short cadence spectroscopic m…
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）
We report the discovery of seven new, very bright gravitational lens systems from our ongoing gravitational lens search, the Sloan Bright Arcs Survey (SBAS). Two of the systems are confirmed to have high source redshifts z=2.19 and z=2.94. Three other systems lie at intermediate redshift with z=1.33,1.82,1.93 and two systems are at low redshift z=0.66,0.86. The lensed source galaxies in all of these systems are bright, with i-band magnitudes ranging from 19.73-22.06. We present the spectrum of each of the source galaxies in these systems along with estimates of the Einstein radius for each sys…
Impact of Large-Scale Structure along Line-of-Sight on Time-Delay Cosmography
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）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；Tianjin Astrophysics Center, Tianjin Normal University（天津师范大学天津天体物理中心）；South-Western Institute for Astronomy Research, Yunnan University（云南大学西南天文研究所）
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）
Degeneracies and modelling choices in double-plane time-delay cosmography
Laboratoire Univers et Particules de Montpellier (LUPM), CNRS & Université de 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）；Université de Genève（日内瓦大学）；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）
Testing Lens Models of PLCK G165.7+67.0 Using Lensed SN H0pe
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；NSF-Simons AI for the Sky (SkAI) Institute（NSF-西蒙斯天空人工智能研究所）；Space Telescope Science Institute（太空望远镜科学研究所）；University of Arizona（亚利桑那大学）；Instituto de Física de Cantabria (CSIC-UC)（坎塔布里亚物理研究所（CSIC-UC））；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge（剑桥大学天文研究所与卡弗里宇宙学研究所）
Gravitational time delays provide a powerful one step measurement of $H_0$, independent of all other probes. One key ingredient in time delay cosmography are high accuracy lens models. Those are currently expensive to obtain, both, in terms of computing and investigator time (10$^{5-6}$ CPU hours and $\sim$ 0.5-1 year, respectively). Major improvements in modeling speed are therefore necessary to exploit the large number of lenses that are forecast to be discovered over the current decade. In order to bypass this roadblock, building on the work by Shajib et al. (2019), we develop an automated …
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…
Context: The gravitational lensing time delay method provides a one-step determination of the Hubble constant (H0) with an uncertainty level on par with the cosmic distance ladder method. However, to further investigate the nature of the dark energy, a H0 estimate down to 1% level is greatly needed. This requires dozens of strongly lensed quasars that are yet to be delivered by ongoing and forthcoming all-sky surveys. Aims: In this work we aim to determine the spectroscopic redshift of PSOJ0147, the first strongly lensed quasar candidate found in the Pan-STARRS survey. The main goal of our wor…
We present the final statistical sample of lensed quasars from the Sloan Digital Sky Survey (SDSS) Quasar Lens Search (SQLS). The well-defined statistical lens sample consists of 26 lensed quasars brighter than i=19.1 and in the redshift range of 0.6<z<2.2 selected from 50,836 spectroscopically confirmed quasars in the SDSS Data Release 7 (DR7), where we restrict the image separation range to 1"<θ<20" and the i-band magnitude differences in two image lenses to be smaller than 1.25 mag. The SDSS DR7 quasar catalog also contains 36 additional lenses identified with various techniques. In additio…
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…
HOLISMOKES -- XVIII. Cosmology with strongly lensed type II supernovae: Effects of instrumental setups on $H_0$
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Technische Universität München（慕尼黑工业大学）；Exzellenzcluster ORIGINS（ORIGINS卓越集群）；STAR Institute（STAR研究所）
We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time delays from strongly lensed quasars currently provide constraints on $H_0$ with < 4% uncertainty, and with 1% within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-dela…
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 develop a robust method to model quadruply lensed quasars, relying heavily on the work of Witt (1996), who showed that for elliptical potentials, the four image positions, the source, and the lensing galaxy lie on a right hyperbola. For the singular isothermal elliptical potential, there exists a complementary ellipse centered on the source which also maps through the four images, with the same axis ratio as the potential but perpendicular to it. We first solve for Witt's hyperbola, reducing the allowable space of models to three dimensions. We then obtain the best fitting complementary ell…
A Targeted Search for Variable Gravitationally Lensed Quasars
University of California, Los Angeles（加州大学洛杉矶分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of San Francisco（旧金山大学）；Gemini Observatory / NSF’s NOIRLab（Gemini 天文台/美国国家科学基金会NOIRLab）；Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo（东京大学 Kavli宇宙物理与数学研究所）；Carnegie Mellon University（卡内基梅隆大学）；University of Hawaii（夏威夷大学）
HST imaging, pipeline modeling, and time-delay predictions of 2 triply-imaged and 15 quadruply-imaged lensed quasars
University of California, Los Angeles（加州大学洛杉矶分校）；STFC Hartree Centre（STFC哈特里中心）；Universidad Andres Bello（安德烈斯贝略大学）；Stony Brook University（石溪大学）；University of Chicago（芝加哥大学）；University of San Francisco（旧金山大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Cambridge（剑桥大学）；Kavli Institute for Cosmology, University of Cambridge（剑桥大学卡弗里宇宙学研究所）；Staples High School（斯塔普尔斯高中）；Universidad de Valparaíso（瓦尔帕莱索大学）
Effects of a central dark matter core on time-delay cosmography with galaxy clusters
Institute of Astronomy and Physics, Inner Mongolia University（内蒙古大学天文与物理学院）；School of Physical Science and Technology, Inner Mongolia University（内蒙古大学物理科学与技术学院）；Center for Frontier Science, Chiba University（千叶大学前沿科学中心）；Department of Physics, Graduate School of Science, Chiba University（千叶大学理学研究科物理学系）
We present a determination of the Hubble constant from the joint, free-form analysis of 8 strongly, quadruply lensing systems. In the concordance cosmology, we find $H_0 = 71.8^{+3.9}_{-3.3}\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ with a precision of $4.97\%$. This is in agreement with the latest measurements from Supernovae Type Ia and Planck observations of the cosmic microwave background. Our precision is lower compared to these and other recent time-delay cosmography determinations, because our modelling strategies reflect the systematic uncertainties of lensing degeneracies. We …
Microlensing not only brings extra magnification lightcurves on top of the intrinsic ones but also shifts them in time domain, making the actual time-delays between images of strongly lensed active galactic nucleus change on the $\sim$ day(s) light-crossing time scale of the emission region. The microlensing-induced time-delays would bias strong lens time-delay cosmography if uncounted. However, due to the uncertainties of the disk size and the disk model, the impact is hard to accurately estimate. In this work, we study how to reduce the bias with designed observation strategy based on a stan…
