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 lens models use well motivated scaling relations between mass and light to incorporate cluster member galaxies, and do not explicitly model line-of-sight structure. Here, we quantify modeling errors due to scatter in the cluster galaxy scaling relations and un-modeled line-of-sight halos. These errors are of the order of a few arcseconds on average for clusters located at typical redshifts (z ~ 0.2 - 0.3). Using Bayesian Markov Chain Monte-Carlo techniques, we show that the inclusion of these modeling errors is critical to deriving unbiased constraints on dark energy. However, when the uncertainties are properly quantified, we show that constraints competitive with other methods may be obtained by combining results from a sample of just 10 simulated clusters with 20 families each. Cosmography with a set of well studied cluster lenses may provide a powerful complementary probe of the dark energy equation of state. Our simulations provide a convenient method of quantifying modeling errors and assessing future strong lensing survey strategies.
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…
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）
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…
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 …
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 …
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…
We investigate the statistics of flux anomalies in gravitationally lensed QSOs as a function of dark matter halo properties such as substructure content and halo ellipticity. We do this by creating a very large number of simulated lenses with finite source sizes to compare with the data. After analyzing these simulations, our conclusions are: 1) The finite size of the source is important. The point source approximation commonly used can cause biased results. 2) The widely used R_cusp statistic is sensitive to halo ellipticity as well as the lens' substructure content. 3) For compact substructu…
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…
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）
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）
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…
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…
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 …
We investigate how strong lensing of dusty, star-forming galaxies by foreground galaxies can be used as a probe of dark matter halo substructure. We find that spatially resolved spectroscopy of lensed sources allows dramatic improvements to measurements of lens parameters. In particular we find that modeling of the full, three-dimensional (angular position and radial velocity) data can significantly facilitate substructure detection, increasing the sensitivity of observables to lower mass subhalos. We carry out simulations of lensed dusty sources observed by early ALMA (Cycle 1) and use a Fish…
The cold dark matter scenario of hierarchical large-scale structure formation predicts the existence of abundant subhalos around large galaxies. However, the number of observed dwarf galaxies is far from this theoretical prediction, suggesting that most of the subhalos could be dark or quite faint. Gravitational lensing is a powerful tool to probe the mass distribution directly irrespective of whether it is visible or dark. Time delay anomalies in strongly lensed quasar systems are complementary to flux ratio anomalies in probing dark matter substructure in galaxies. Here we propose that lense…
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…
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…
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 …
We study the application of machine learning techniques for the detection of the astrometric signature of dark matter substructure. In this proof of principle a population of dark matter subhalos in the Milky Way will act as lenses for sources of extragalactic origin such as quasars. We train {\it ResNet-18}, a state-of-the-art convolutional neural network to classify angular velocity maps of a population of quasars into lensed and no lensed classes. We show that an SKA -like survey with extended operational baseline can be used to probe the substructure content of the Milky Way, and demonstra…
In recent years, it has become possible to detect individual dark matter subhalos near images of strongly lensed extended background galaxies. Typically, only the most massive subhalos in the strong lensing region may be detected this way. In this work, we show that strong lenses may also be used to constrain the much more numerous population of lower mass subhalos that are too small to be detected individually. In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing. We develop the mathematical framewo…
Strong gravitational lensing effect is a powerful tool to probe cosmological models and gravity theories. Recently, the time-delay cosmography from strong lensing and the stellar kinematics of the deflector, which encode the Hubble constant and the post-Newtonian parameter via two distance ratios reflecting the lensing mass and dynamical mass respectively, have been proposed to investigate these two parameters simultaneously. Among strong lensing systems with different sources, strongly lensed fast radio bursts (FRBs) have been proposed as precision probes of the universe since the time delay …
A Bayesian statistical formalism is developed to quantify the level at which the mass function slope (alpha) and the projected cumulative mass fraction (f) of (CDM) substructure in strong gravitational-lens galaxies, with arcs or Einstein rings, can be recovered as function of the lens-survey parameters and the detection threshold of the substructure mass. The method is applied to different sets of mock data to explore a range of observational limits: (i) the number of lens galaxies in the survey, (ii) the mass threshold, Mlow, for the detection of substructures and (iii) the uncertainty of th…
The subtle and unique imprint of dark matter substructure on extended arcs in strong lensing systems contains a wealth of information about the properties and distribution of dark matter on small scales and, consequently, about the underlying particle physics. However, teasing out this effect poses a significant challenge since the likelihood function for realistic simulations of population-level parameters is intractable. We apply recently-developed simulation-based inference techniques to the problem of substructure inference in galaxy-galaxy strong lenses. By leveraging additional informati…
We study the abundance of substructure in the matter density near galaxies using ALMA Science Verification observations of the strong lensing system SDP.81. We present a method to measure the abundance of subhalos around galaxies using interferometric observations of gravitational lenses. Using simulated ALMA observations, we explore the effects of various systematics, including antenna phase errors and source priors, and show how such errors may be measured or marginalized. We apply our formalism to ALMA observations of SDP.81. We find evidence for the presence of a $M=10^{8.96\pm 0.12} M_{\o…
We map the lensing-inferred substructure in the first three clusters observed by the Hubble Space Telescope Frontier Fields Initiative (HSTFF): Abell 2744 (z = 0.308), MACSJ0416, (z = 0.396) and MACSJ1149 (z = 0.543). Statistically resolving dark-matter subhaloes down to ~10^{9.5} solar masses, we compare the derived subhalo mass functions (SHMFs) to theoretical predictions from analytical models and with numerical simulations in a Lambda Cold Dark Matter (LCDM) cosmology. Mimicking our observational cluster member selection criteria in the HSTFF, we report excellent agreement in both amplitud…
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 …
Mass clumps in gravitational lens galaxies can perturb lensed images in characteristic ways. Strong lens flux ratios have been used to constrain the amount of dark matter substructure in lens galaxies, and various other observables have been considered as additional probes of substructure. We study the general theory of lensing with stochastic substructure in order to understand how lensing observables depend on the mass function and spatial distribution of clumps. We find that magnification perturbations are mainly sensitive to the total mass in substructure projected near the lensed images; …
Strong gravitational lensing observations can test structure formation models by constraining the masses and concentrations of subhaloes in massive galaxy clusters. Recent work has concluded that cluster subhaloes are more abundant and/or concentrated than predicted by $Λ$CDM simulations; this finding has been interpreted as arising from unidentified issues with simulations or an incorrect understanding of the nature of dark matter. We test these hypotheses by comparing observed subhalo masses and maximum circular velocities $v_\mathrm{max}$ to predictions from the high resolution Hydrangea ga…
Gravitational lens flux-ratio anomalies provide a powerful technique for measuring dark matter substructure in distant galaxies. However, before using these flux-ratio anomalies to test galaxy formation models, it is imperative to ascertain that the given anomalies are indeed due to the presence of dark matter substructure and not due to some other component of the lensing galaxy halo or to propagation effects. Here we present the case of CLASS~B1555+375, which has a strong radio-wavelength flux-ratio anomaly. Our high-resolution near-infrared Keck~II adaptive optics imaging and archival Hubbl…
Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos ($<10^{10} M_\odot$) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large datasets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST's COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator o…
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…
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）
Cold dark matter (CDM) constitutes most of the matter in the Universe. The interplay between dark and luminous matter in dense cosmic environments like galaxy clusters is studied theoretically using cosmological simulations. Observed gravitational lensing is used to test and characterize the properties of substructures - the small-scale distribution of dark matter - in clusters. An apt metric, the probability of strong lensing events produced by dark matter substructure, is devised and computed for 11 galaxy clusters. We report that observed cluster substructures are more efficient lenses than…
Dark halo substructure may reveal itself through secondary, small-scale gravitational lensing effects on light sources that are macrolensed by a foreground galaxy. Here, we explore the prospects of using Very Long Baseline Interferometry (VLBI) observations of multiply-imaged quasar jets to search for submilliarcsecond-scale image distortions produced by various forms of dark substructures in the 1e3-1e8 Msolar mass range. We present lensing simulations relevant for the angular resolutions attainable with the existing European VLBI Network (EVN), the global VLBI array, and an upcoming observin…
The Hubble Frontier Fields (HFF) are six clusters of galaxies, all showing indications of recent mergers, which have recently been observed for lensed images. As such they are the natural laboratories to study the merging history of galaxy clusters. In this work, we explore the 2D power spectrum of the mass distribution $P_{\rm M}(k)$ as a measure of substructure. We compare $P_{\rm M}(k)$ of these clusters (obtained using strong gravitational lensing) to that of $Λ$CDM simulated clusters of similar mass. To compute lensing $P_{\rm M}(k)$, we produced free-form lensing mass reconstructions of …
Gravitational wave experiments have entered a new stage which gets us closer to the opening a new observational window on the Universe. In particular, the Einstein Telescope (ET) is designed to have a fantastic sensitivity that will provide with tens or hundreds of thousand NS-NS inspiral events per year up to the redshift z = 2. Some of such events should be gravitationally lensed by intervening galaxies. We explore the prospects of observing gravitationally lensed inspiral NS-NS events in the Einstein telescope. Being conservative we consider the lens population of elliptical galaxies. It tu…
We investigate the spectro-photometric variability of quasars due to lensing of small mass substructure (from several tens to several hundreds solar masses). The aim of this paper is to explore the milli/microlensing influence on the flux anomaly observed between images of a lensed quasar in different spectral bands and possible influence of small mass structure lensing of non-macrolensed quasars.We find that spectro-photometric variability may be also caused by lensing of small mass diffuse structure and can produce the flux anomaly which is sometimes seen in different images of a lensed quas…
Recently, Meneghetti et al. reported an excess of small-scale gravitational lenses in galaxy clusters. We study its implications for self-interacting dark matter (SIDM), compared with standard cold dark matter (CDM). We design controlled N-body simulations that incorporate observational constraints. The presence of early-type galaxies in cluster substructures can deepen gravitational potential and reduce tidal mass loss. Both scenarios require a relatively high baryon concentration in the substructure to accommodate the lensing measurements, and their tangential caustics are similar. The SIDM …
We present an analysis of seven strongly gravitationally lensed quasars and the corresponding constraints on the properties of dark matter. Our results are derived by modelling the lensed image positions and flux-ratios using a combination of smooth macro models and a population of low-mass haloes within the mass range 10^6 to 10^9 Msun. Our lens models explicitly include higher-order complexity in the form of stellar discs and luminous satellites, as well as low-mass haloes located along the observed lines of sight for the first time. Assuming a Cold Dark Matter (CDM) cosmology, we infer an a…
Impact on time delays due to milli-lensing by subhalos on lensed gravitational waves
Department of Physics, Dr. Vishwanath Karad MIT World Peace University（德拉·维斯瓦纳特·卡拉德麻省理工学院世界和平大学物理系）；Inter-University Centre for Astronomy and Astrophysics（大学间天文学和天体物理学中心）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（卡弗里宇宙物理学与数学起源研究所（WPI），东京大学宇宙射线研究所）；Department of Physics, Indian Institute of Science Education and Research（印度科学教育与研究机构物理系）
Studying the smallest self-bound dark matter structure in our Universe can yield important clues about the fundamental particle nature of dark matter. Galaxy-scale strong gravitational lensing provides a unique way to detect and characterize dark matter substructures at cosmological distances from the Milky Way. Within the cold dark matter (CDM) paradigm, the number of low-mass subhalos within lens galaxies is expected to be large, implying that their contribution to the lensing convergence field is approximately Gaussian and could thus be described by their power spectrum. We develop here a g…
The analysis of optical images of galaxy-galaxy strong gravitational lensing systems can provide important information about the distribution of dark matter at small scales. However, the modeling and statistical analysis of these images is extraordinarily complex, bringing together source image and main lens reconstruction, hyper-parameter optimization, and the marginalization over small-scale structure realizations. We present here a new analysis pipeline that tackles these diverse challenges by bringing together many recent machine learning developments in one coherent approach, including va…
(abridged) Gravitationally lensed quasars can be used as powerful cosmological and astrophysical probes. We can (i) infer the Hubble constant based on the time-delay technique, (ii) unveil substructures along the l.o.s. toward distant galaxies, and (iii) compare the shape and the slope of baryons and dark matter distributions in galaxies. To reach these goals, we need high-accuracy astrometry and morphology measurements of the lens. In this work, we first present new astrometry for 11 lenses with measured time delays. Using MCS deconvolution on NIC2 HST images, we reached an astrometric accura…
The cold dark matter (CDM) cosmological model unambigously predicts that a large number of haloes should survive as subhaloes when they are accreted into a larger halo. The CDM model would be ruled out if such substructures were shown not to exist. By contrast, if the dark matter consists of warm particles (WDM), then below a threshold mass that depends on the particle mass far fewer substructures would be present. Finding subhaloes below a certain mass would then rule out warm particle masses below some value. Strong gravitational lensing provides a clean method to measure the subhalo mass fu…
We introduce a machine learning method for estimating the sensitivity of strong lens observations to dark matter subhaloes in the lens. Our training data include elliptical power-law lenses, Hubble Deep Field sources, external shear, and noise and PSF for the Euclid VIS instrument. We set the concentration of the subhaloes using a $v_\mathrm{max}$-$r_\mathrm{max}$ relation. We then estimate the dark matter subhalo sensitivity in $16{,}000$ simulated strong lens observations with depth and resolution resembling Euclid VIS images. We find that, with a $3σ$ detection threshold, $2.35$ per cent of…
