Strong gravitational lensing of variable sources, such as quasars or supernovae, can be used to constrain cosmological parameters through a technique known as "time-delay cosmography''. Competitive constraints on the Hubble constant have been achieved with electromagnetic observations of lensed quasars and lensed supernovae. Gravitational wave (GW) astronomy may open up a new channel for time-delay cosmography with GW signal replacing the electromagnetic (EM) one. We highlight the similarities of using GW signals to be applied to time-delay cosmography compared to EM signal. We then discuss key differences between GW and EM signals and their resulting advantages and inconveniences from the angle of the current state-of-the-art using quasars and lensed supernovae for time-delay cosmography. We identify the astrometric precision requirement of the images as a key challenge to overcome and highlight the potentially significant impact that near-perfect time-delay measurements of lensed GWs can bring to the table.
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 …
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…
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…
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…
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 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…
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 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 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…
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…
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 …
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…
Strong lensing time delay cosmography has excellent complementarity with other dark energy probes, and will soon have abundant systems detected. We investigate two issues in the imaging and spectroscopic followup required to obtain the time delay distance. The first is optimization of spectroscopic resources. We develop a code to optimize the cosmological leverage under the constraint of constant spectroscopic time, and find that sculpting the lens system redshift distribution can deliver a 40% improvement in dark energy figure of merit. The second is the role of systematics, correlated betwee…
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…
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…
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…
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 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…
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 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 …
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 …
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）
Standard Shapiro delay-based test of the equivalence principle, which are grounded on the measurement of two arrival times from a unique source but from messengers with different properties, cannot produce a reliable quantitative test of the Einstein equivalence principle. Essentially because they are based on the estimation for different messengers of the one-way propagation time between the emission and the observation that is not an observable per se. As a consequence, such tests are extremely model dependent, at best. In what follows, I argue that the differential arrival times for strongl…
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）
We present a new idea of testing the validity of the Friedman-Lema\^ıtre-Robertson-Walker metric, through the multiple measurements of galactic-scale strong gravitational lensing systems with type Ia supernovae in the role of sources. Each individual lensing system will provide a model-independent measurement of the spatial curvature parameter referring only to geometrical optics independently of the matter content of the universe. This will create a valuable opportunity to test the FLRW metric directly. Our results show that with hundreds of strongly lensed SNe Ia observed by LSST, one would …
General relativity (GR) predicts concordant trajectories for photons and gravitational waves (GW). We propose a new multi-messenger avenue (GW-CMB-CMB) to prove this aspect of fundamental physics by cross-correlating the GW signal of astrophysical origin with the lensing field derived from the cosmic microwave background (CMB). This new window will allow robust measurement of the prediction from GR with high signal-to-noise and will be able to unveil the true nature of gravity using the GW sources detected by missions such as the Laser Interferometer Space Antenna (LISA), Einstein Telescope an…
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…
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…
We investigate the potential of high-energy astrophysical events, from which both massless and massive signals are detected, to probe fundamental physics. In particular, we consider how strong gravitational lensing can induce time delays in multi-messenger signals originating from the same source. Obvious messenger examples are massless photons and gravitational waves, and massive neutrinos, although more exotic applications can also be imagined, such as to massive gravitons or axions. The different propagation times of the massive and massless particles can, in principle, place bounds on the …
In the coming LSST era, we will observe $\mathcal{O}(100)$ of lensed supernovae (SNe). In this paper, we investigate possibility for predicting time and sky position of a supernova using strong lensing. We find that it will be possible to predict the time and position of the fourth image of SNe which produce four images by strong lensing, with combined information from the three previous images. It is useful to perform multi-messenger observations of the very early phase of supernova explosions including the shock breakout.
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）
The recent detection of gravitational waves (GWs) and electromagnetic (EM) waves originating from the same source marks the start of a new multi-messenger era in astronomy. The arrival time difference between the GW and EM signal can be used to constrain differences in their propagation speed, and thus gravitational theories. We study to what extent a non-zero time delay can be explained by gravitational lensing when the line of sight to the source passes near a massive object. For galaxy scale lenses, this delay becomes relevant for GWs with frequencies between $10^{-6}$ and $10^{-9}$ Hz, sou…
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…
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 …
Gamma-ray bursts (GRBs) are attractive objects for constraining the nature of dark energy in a way complementary to other cosmological probes, especially at high redshifts. However, the apparent magnitude of distant GRBs can be distorted by the gravitational lensing from the density fluctuations along the line of sight. We investigate the gravitational lensing effect on the cosmological parameters and dark energy equation of state from GRBs. We first calibrated the GRB luminosity relations without assuming any cosmological models. The luminosity distances of low-redshift GRBs were calibrated w…
In light of the newly opened and rapidly growing gravitational waves window in multi-messenger astronomy, in order to fully take advantage of the new opportunities we are provided with, new ideas are required for a better and deeper employ of the state-of-the-art probes we handle. Following this goal, here we suggest a method to constrain the cosmological background, and the Hubble constant in particular, by future observations of gravitationally lensed radiation emitted by a single source in both the gravitational wave and the electromagnetic regimes. The lensing of the gravitational wave rad…
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…
