We present a simple and promising new method to measure the expansion rate and the geometry of the universe that combines observations related to the time delays between the multiple images of time-varying sources, strongly lensed by galaxy clusters, and Type Ia supernovae, exploding in galaxies belonging to the same lens clusters. By means of two different statistical techniques that adopt realistic errors on the relevant quantities, we quantify the accuracy of the inferred cosmological parameter values. We show that the estimate of the Hubble constant is robust and competitive, and depends only mildly on the chosen cosmological model. Remarkably, the two probes separately produce confidence regions on the cosmological parameter planes that are oriented in complementary ways, thus providing in combination valuable information on the values of the other cosmological parameters. We conclude by illustrating the immediate observational feasibility of the proposed joint method in a well-studied lens galaxy cluster, with a relatively small investment of telescope time for monitoring from a 2 to 3m class ground-based telescope.
The time delay between the arrival of photons of multiple images of time variable sources can be used to constrain absolute distances in the Universe (Refsdal 1964), and in turn obtain a direct estimate of the Hubble constant and other cosmological parameters. To convert the time delay into distances, it is well known that the gravitational potential of the main deflector and the contribution of the matter along the line-of-sight need to be known to a sufficient level of precision. In this paper, we discuss a new astrometric requirement that is becoming important as time-delay cosmography impr…
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…
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…
Multiply imaged time-variable sources can be used to measure absolute distances as a function of redshifts and thus determine cosmological parameters, chiefly the Hubble Constant H$_0$. In the two decades up to 2020, through a number of observational and conceptual breakthroughs, this so-called time-delay cosmography has reached a precision sufficient to be an important independent voice in the current ``Hubble tension'' debate between early- and late-universe determinations of H$_0$. The 2020s promise to deliver major advances in time-delay cosmography, owing to the large number of lenses to …
Using a new sub-sample of observed strong gravitational lens systems, for the first time, we present the equation for the angular diameter distance in the $y$-redshift scenario for cosmography and use it to test the cosmographic parameters. In addition, we also use the observational Hubble data from cosmic chronometers and a Joint analysis of both data is performed. Among the most important conclusions are that this new analysis for cosmography using Strong Lensing Systems is equally competitive to constrain the cosmographic parameters as others presented in literature. Additionally, we presen…
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…
Cluster strong lensing cosmography is a promising probe of the background geometry of the Universe and several studies have emerged, thanks to the increased quality of observations using space and ground-based telescopes. For the first time, we use a sample of five cluster strong lenses to measure the values of cosmological parameters and combine them with those from classical probes. In order to assess the degeneracies and the effectiveness of strong-lensing cosmography in constraining the background geometry of the Universe, we adopt four cosmological scenarios. We find good constraining pow…
Inferring cosmological parameters from time-delay strong lenses requires a significant investment of telescope time; it is therefore tempting to focus on the systems with the brightest sources, the highest image multiplicities and the widest image separations. We investigate if this selection bias can influence the properties of the lenses studied and the cosmological parameters that are inferred. Using a population of lenses with ellipsoidal powerlaw density profiles, we build a sample of double and quadruple image systems. Assuming reasonable thresholds on image separation and flux, based on…
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）
In this paper we probe five cosmological models for which the dark energy equation of state parameter, $w(z)$, is parameterized as a function of redshift using strong lensing data in the galaxy cluster Abell 1689. We constrain the parameters of the $w(z)$ functions by reconstructing the lens model under each one of these cosmologies with strong lensing measurements from two galaxy clusters: Abell 1689 and a mock cluster, Ares, from the Hubble Frontier Fields Comparison Challenge, to validate our methodology. To quantify how the cosmological constraints are biased due to systematic effects in t…
The time delays between the multiple images of a strong lens system, together with a model of the lens mass distribution, allow a one-step measurement of a cosmological distance, namely, the "time-delay distance" of the lens (D_dt) that encodes cosmological information. The time-delay distance depends sensitively on the radial profile slope of the lens mass distribution; consequently, the lens slope must be accurately constrained for cosmological studies. We show that the slope cannot be constrained in two-image systems with single-component compact sources, whereas it can be constrained in sy…
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…
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）
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 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…
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 …
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…
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…
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…
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…
We perform a comprehensive study of the total mass distribution of the galaxy cluster RXCJ2248 ($z=0.348$) with a set of high-precision strong lensing models, which take advantage of extensive spectroscopic information on many multiply lensed systems. In the effort to understand and quantify inherent systematics in parametric strong lensing modelling, we explore a collection of 22 models where we use different samples of multiple image families, parametrizations of the mass distribution and cosmological parameters. As input information for the strong lensing models, we use the CLASH HST imagin…
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…
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 re…
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…
Strong gravitational lensing by galaxy clusters is a fundamental tool to study dark matter and constrain the geometry of the Universe. Recently, the Hubble Space Telescope Frontier Fields programme has allowed a significant improvement of mass and magnification measurements but lensing models still have a residual root mean square between 0.2 arcsec and few arcsec- onds, not yet completely understood. Systematic errors have to be better understood and treated in order to use strong lensing clusters as reliable cosmological probes. We have analysed two simulated Hubble-Frontier-Fields-like clus…
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 …
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）
Strong lensing time-delay systems constrain cosmological parameters via the so-called time-delay distance and the angular diameter distance to the lens. In previous studies, only the former information was used. In this paper, we show that the cosmological constraints improve significantly when the latter information is also included. Specifically, the angular diameter distance plays a crucial role in breaking the degeneracy between the curvature of the Universe and the time-varying equation of state of dark energy. Using a mock sample of 55 bright quadruple lens systems based on expectations …
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 …
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）
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…
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）
Cosmography provides a direct method to map the expansion history of the Universe in a model-independent way. Recently, different kinds of observations have been used in cosmographic analyses, such as SNe Ia and gamma ray bursts measurements, weak and strong lensing, cosmic microwave background anisotropies, etc. In this work we examine the prospects for constraining cosmographic parameters from current and future measurements of galaxy clusters distances based on their Sunyaev-Zeldovich effect (SZE) and X-ray observations. By assuming the current observational error distribution, we perform M…
Accurate and precise measurements of the Hubble constant are critical for testing our current standard cosmological model and revealing possibly new physics. With Hubble Space Telescope (HST) imaging, each strong gravitational lens system with measured time delays can allow one to determine the Hubble constant with an uncertainty of $\sim 7\%$. Since HST will not last forever, we explore adaptive-optics (AO) imaging as an alternative that can provide higher angular resolution than HST imaging but has a less stable point spread function (PSF) due to atmospheric distortion. To make AO imaging us…
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…
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…
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）
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…
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）
UUsing a five-hour adaptive-optics-assisted observation with MUSE, we have identified a doubly-imaged Ly alpha source at redshift 5.975 behind the z=0.222 lens galaxy J0946+1006 ('the Jackpot'). The source separation implies an Einstein radius of ~2.5 arcsec. Combined with the two previously-known Einstein rings in this lens (radii 1.4 arcsec at z = 0.609 and 2.1 arcsec at z ~ 2.4), this system is now a unique galaxy-scale triple-source-plane lens. We show that existing lensing models for J0946+1006 successfully map the two new observed images to a common point on the z=5.975 source plane. The…
