Modifications to GR generically predict time and scale-dependent effects which may be probed by observations of strong lensing by galaxies. Measurements of the stellar velocity dispersion determine the dynamical mass whereas measurements of the Einstein radius determine the lensing mass. In GR these two masses are equal; in alternative gravity theories they may not be. Using measurements of the stellar velocity dispersion and strong lensing around galaxies from the Sloan Lens ACS (SLACS) survey we place constraints on lensing in modified gravity theories and extend previous studies by applying this data to explore its dependence on various properties of the lens such as the lens redshift or mass and thereby constrain scalar-tensor, f(R) gravity theories, and generic parameterizations of deviations from GR. Besides applying the observations to these specific gravity theories, the data places a constraint on a generic dependence of modifications to GR on the lens mass and redshift. At the 68% confidence level we find that the ratio between the lensing and dynamical masses can only vary by less then 50% over a mass range for the lens galaxies of 1E12 < M/Msun < 1E14 and less than 40% over the redshift range 0.06 < z < 0.36.
Modified gravitational wave propagation is a smoking gun of modifications of gravity at cosmological scales, and can be the most promising observable for testing such theories. The observation of gravitational waves (GW) in recent years has allowed us to start probing this effect, and here we briefly review two promising ways of testing it. We will show that, already with the current network of detectors, it is possible to reach an interesting accuracy in the estimation of the $Ξ_0$ parameter (that characterizes modified gravitational wave propagation, with $Ξ_{0, {\rm GR}} = 1$) and with next…
Probing the speed of light is as an important test of General Relativity but the measurements of $c$ using objects in the distant universe have been almost completely unexplored. In this letter, we propose an idea to use the multiple measurements of galactic-scale strong gravitational lensing systems with type Ia supernova acting as background sources to estimate the speed of light. This provides an original method to measure the speed of light using objects located at different redshifts which emitted their light in a distant past. Moreover, we predict that strongly lensed SNe Ia observed by …
We devise a test of nonlinear departures from general relativity (GR) using time delays in strong gravitational lenses. We use a phenomenological model of gravitational screening as a step discontinuity in the measure of curvature per unit mass, at a radius $Λ$. The resulting slip between two scalar gravitational potentials leads to a shift in the apparent positions and time delays of lensed sources, relative to the GR predictions, of size $γ_{\rm PN}-1$. As a proof of principle, we use measurements of two lenses, RXJ1121-1231 and B1608+656, to constrain deviations from GR to be below $|γ_{\rm…
Strong gravitational lensing by galaxies provides us with a unique opportunity to understand the nature of gravity on galactic and extra-galactic scales. In this paper, we propose a new multimessenger approach using data from both gravitational wave (GW) and the corresponding electromagnetic (EM) counterpart to infer the constraint of the modified gravity (MG) theory denoted by the scale dependent phenomenological parameter. To demonstrate the robustness of this approach, we calculate the time-delay predictions by choosing various values of the phenomenological parameters and then compare them…
Using the combined resolving power of the Hubble Space Telescope and gravitational lensing, we resolve star-forming structures in a z~2.5 galaxy on scales much smaller than the usual kiloparsec diffraction limit of HST. SGAS J111020.0+645950.8 is a clumpy, star forming galaxy lensed by the galaxy cluster SDSS J1110+6459 at z = 0.659, with a total magnification ~30x across the entire arc. We use a hybrid parametric/non-parametric strong lensing mass model to compute the deflection and magnification of this giant arc, reconstruct the light distribution of the lensed galaxy in the source plane, a…
We present rest-frame optical spectra for a sample of 9 low-mass star-forming galaxies in the redshift range 1.5 < z < 3 which are gravitationally lensed by foreground clusters. We used Triplespec, an echelle spectrograph at the Palomar 200-inch telescope that is very effective for this purpose as it samples the entire near-infrared spectrum simultaneously. By measuring the flux of nebular emission lines we derive gas phase metallicities and star formation rates, and by fitting the optical to infrared spectral energy distributions we obtain stellar masses. Taking advantage of the high magnific…
Probing the relative speeds of gravitational waves and light acts as an important test of General Relativity and alternative theories of gravity. Measuring the arrival time of gravitational waves and electromagnetic counterparts can be used to measure the relative speeds, but only if the intrinsic time-lag between emission of the photons and gravitational waves is well understood. Here we suggest a method that does not make such an assumption, using future strongly lensed GW events and EM counterparts; Biesiada et al forecast that 50-100 strongly lensed GW events will be observed each year wit…
Direct measurements of dark matter distributions in galaxies are currently only possible through the use of gravitational lensing observations. Combinations of lens modelling and stellar velocity dispersion measurements provide the best constraints on dark matter distributions in individual galaxies, however they can be quite complex. In this paper, we use observations and simulations of gravitational microlensing to measure the smooth (dark) matter mass fraction at the position of lensed images in three lens galaxies: MG 0414+0534, SDSS J0924+0219 and Q2237+0305. The first two systems consist…
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）
We study the redshift distribution of two samples of early-type gravitational lenses, extracted from a larger collection of 122 systems, to constrain the cosmological constant in the LCDM model and the parameters of a set of alternative dark energy models (XCDM, Dvali-Gabadadze-Porrati and Ricci dark energy models), under a spatially flat universe. The likelihood is maximized for $Ω_Λ= 0.70 \pm 0.09$ when considering the sample excluding the SLACS systems (known to be biased towards large image-separation lenses) and no-evolution, and $Ω_Λ= 0.81\pm 0.05$ when limiting to gravitational lenses w…
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 …
We consider gravitational wave (GW) sources with an associated electromagnetic (EM) counterpart, and analyze the time delay between both signals in the presence of lensing. If GWs have wavelengths comparable to the Schwarzschild radius of astrophysical lenses, they must be treated with wave optics, whereas EM waves are typically well within the approximation of geometric optics. With concrete examples, we confirm that the GW signal never arrives before its EM counterpart, if both are emitted at the same time. However, during the inspiral of a binary, peaks of the GW waveform can arrive before …
We re-examine claims of redshift evolution in black hole-bulge scaling relations based on lensed quasars. In particular, we refine the black hole mass estimates using measurements of Balmer lines from near-infrared spectroscopy obtained with Triplespec at Apache Point Observatory. In support of previous work, we find a large scatter between Balmer and UV line widths, both MgII 2796, 2803 and CIV 1548, 1550. There is tentative evidence that CIII] 1909, despite being a blend of multiple transitions, may correlate well with MgII, although a larger sample is needed for a real calibration. Most imp…
Galaxy-scale strong gravitational lenses with measured stellar velocity dispersions allow a test of the weak-field metric on kiloparsec scales and a geometric measurement of the cosmological distance-redshift relation, provided that the mass-dynamical structure of the lensing galaxies can be independently constrained to a sufficient degree. We combine data on 53 galaxy-scale strong lenses from the Sloan Lens ACS Survey with a well-motivated fiducial set of lens-galaxy parameters to find (1) a constraint on the post-Newtonian parameter gamma = 1.01 +/- 0.05 and (2) a determination of Omega_Lamb…
The positions of images produced by the gravitational lensing of background sources provide unique insight in to galaxy-lens mass distribution. However, even quad images of extended sources are not able to fully characterize the central regions of the host galaxy. Most previous work has focused either on the radial density profile of the lenses or localized substructure clumps. Here, we concentrate on the azimuthal mass asymmetries near the image circle. The motivation for considering such mass inhomogeneities is that the transition between the central stellar dominated region and the outer da…
The assumptions of large-scale homogeneity and isotropy underly the familiar Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) metric that appears to be an accurate description of our Universe. In this paper, we propose a new strategy of testing the validity of the FLRW metric, based on the galactic-scale lensing systems where strongly lensed gravitational waves and their electromagnetic counterparts can be simultaneously detected. Each strong lensing system creates opportunity to infer the curvature parameter of the Universe. Consequently, combined analysis of many such systems will provide a mode…
Strong lensing provides popular techniques to investigate the mass distribution of intermediate redshift galaxies, testing galaxy evolution and formation scenarios. It especially probes the background cosmic expansion, hence constraining cosmological parameters. The measurement of Einstein radii and central velocity dispersions indeed allows to trace the ratio D_s/D_ls between the distance D_s from the observer to the source and the distance D_ls from the lens to the source. We present an improved method to explicitly include the two - component structure in the galaxy lens modeling, in order …
Study of dark interactions through strong gravitational lenses
Facultad de Ingeniería y Arquitectura, Universidad Central de Chile（智利中央大学工程与建筑学院）；Observatorio Astronómico Nacional, Universidad Nacional Autónoma de México（墨西哥国立自治大学国家天文台）
MOND predicts that the asymptotic gravitational potential of an isolated, bounded (baryonic) mass, M, is phi(r)=(MGa0)^{1/2}ln(r); a0 is the MOND constant. Relativistic MOND theories predict that the lensing effects of M are dictated by phi(r) as general-relativity lensing is dictated by the Newtonian potential. Thus, MOND predicts that the asymptotic Newtonian potential deduced from galaxy-galaxy gravitational lensing will have: (1) a logarithmic r dependence, and (2) a normalization (parametrized standardly as 2s^2) that depends only on M: s=(MGa0/4)^{1/4}. I compare these predictions with r…
Flexion is the weak lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. The flexion signal-to-noise ratio can be an order of magnitude larger than that of shear. For the first time, we show how this makes flexion an invaluable tool for discriminating among alternative cosmological models. We analyse a scalar field model of unified dark matter and dark energy, a brane-world cosmology and two f(R) modified-action theories. We show that these models can be distinguished from LCDM at several standard deviations by measuring the power spectrum of cosmic flex…
Acting as powerful gravitational lenses, the strong lensing galaxy clusters of the deep Hubble Frontier Fields (HFF) program permit access to lower-luminosity galaxies lying at higher redshifts than hitherto possible. We analyzed the HFF to measure the volume density of Lyman-break galaxies at $z > 4.75$ by identifying a complete and reliable sample up to $z \simeq 10$. A marked deficit of such galaxies was uncovered in the highly magnified regions of the clusters relative to their outskirts, implying that the magnification of the sky area dominates over additional faint galaxies magnified abo…
We examine the flux density ratio anomaly in the quadruply-imaged strong gravitational lens, B1422+231, and consider the contribution of $10-10^3M_{\odot}$ primordial black holes (PBHs) as a potential dark matter constituent. We describe the first flux density ratio measurement of B1422+231 in the millimeter-wave band using the Atacama Large Millimeter Array (ALMA). This fills an important multi-wavelength gap in our knowledge of this key lensed system. The flux density of the quasar at 233 GHz is dominated by synchrotron emission and the source size is estimated to be 66.9 pc. The observed fl…
In these lectures I give an overview of gravitational lensing, concentrating on theoretical aspects, including derivations of some of the important results. Topics covered include the determination of surface mass densities of intervening lenses, as well as the statistical analysis of distortions of galaxy images by general inhomogeneities (cosmic shear), both in 2D projection on the sky, and in 3D where source distance information is available. 3D mass reconstruction and the shear ratio test are also considered, and the sensitivity of observables to Dark Energy is used to show how its equatio…
We report the results of $EasyCritics$, a fully automated algorithm for the efficient search of strong-lensing (SL) regions in wide-field surveys, applied to the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). By using only the photometric information of the brightest elliptical galaxies distributed over a wide redshift range ($\smash{0.2 \lesssim z \lesssim 0.9}$) and without requiring the identification of arcs, our algorithm produces lensing potential models and catalogs of critical curves of the entire survey area. We explore several parameter set configurations in order to test …
Joint constraints on gravity and stellar orbital anisotropy in massive galaxies
Shanghai Normal University（上海师范大学）；National Astronomical Observatories, Chinese Academy of Science（中国科学院国家天文台）；Purple Mountain Observatory, Chinese Academy of Science（中国科学院紫金山天文台）；South-Western Institute for Astronomy Research, Yunnan University（云南大学西南天文研究所）；Shanghai Astronomical Observatory, Chinese Academy of Science（中国科学院上海天文台）
Inspired by a new compilation of strong lensing systems, which consist of 204 points in the redshift range $0.0625< z_{l} < 0.958$ for the lens and $0.196< z_{s} < 3.595$ for the source, we constrain three models that generate a late cosmic acceleration: the $ω$-cold dark matter model, the Chevallier-Polarski-Linder and the Jassal-Bagla-Padmanabhan parametrizations. Our compilation contains only those systems with early type galaxies acting as lenses, with spectroscopically measured stellar velocity dispersions, estimated Einstein radius, and both the lens and source redshifts. We assume an ax…
Based on a mass-selected sample of galaxy-scale strong gravitational lenses from the SLACS, BELLS, LSD and SL2S surveys and using a well-motivated fiducial set of lens-galaxy parameters we tested the weak-field metric on kiloparsec scales and found a constraint on the post-Newtonian parameter $γ= 0.995^{+0.037}_{-0.047}$ under the assumption of a flat $Λ$CDM universe with parameters taken from \textit{Planck} observations. General relativity (GR) predicts exactly $γ=1$. Uncertainties concerning the total mass density profile, anisotropy of the velocity dispersion and the shape of the light-pro…
Strong gravitational lensing can be used to directly measure the mass function of their satellites, thus testing one of the fundamental predictions of cold dark matter cosmological models. Given the importance of this test it is essential to ensure that galaxies acting as strong lenses have dark and luminous satellites which are representative of the overall galaxy population. We address this issue by measuring the number and spatial distribution of luminous satellites in ACS imaging around lens galaxies from the Sloan Lens Advanced Camera for Surveys (SLACS) lenses, and comparing them with th…
For nearly 40 years, dark matter has been widely assumed to be cold and collisionless. Cold dark matter models make fundamental predictions for the behavior of dark matter on small (<10 kpc) scales. These predictions include cuspy density profiles at the centers of dark matter halos and a halo mass function that increases as dN/dM ~ M^-1.9 down to very small masses. We suggest two observational programs relying on extremely large telescopes to critically test these predictions, and thus shed new light on the nature of dark matter. (1) Combining adaptive optics-enabled imaging with deep spectro…
Extragalactic test of General Relativity with time-delay gravitational lenses
Beijing Normal University（北京师范大学）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京天体物理前沿研究院）；National Centre for Nuclear Research（国家核研究中心）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Physics and Optoelectronic, Yangtze University（长江大学物理与电子信息学院）
We reconstruct the projected mass distribution of a massive merging Hubble Frontier Fields cluster MACSJ0416 using the genetic algorithm based free-form technique called Grale. The reconstructions are constrained by 149 lensed images identified by Jauzac et al. using HFF data. No information about cluster galaxies or light is used, which makes our reconstruction unique in this regard. Using visual inspection of the maps, as well as galaxy-mass correlation functions we conclude that overall light does follow mass. Furthermore, the fact that brighter galaxies are more strongly clustered with mas…
Einstein's theory of general relativity (GR) has been precisely tested on solar system scales, but extragalactic tests are still poorly performed. In this work, we use a newly compiled sample of galaxy-scale strong gravitational lenses to test the validity of GR on kiloparsec scales. In order to solve the circularity problem caused by the preassumption of a specific cosmological model based on GR, we employ the distance sum rule in the Friedmann-Lema\^ıtre-Robertson-Walker metric to directly estimate the parameterized post-Newtonian (PPN) parameter $γ_{\rm PPN}$ and the cosmic curvature $Ω_k$ …
Testing General Relativity on Galactic Scales via DESI-BAO and Strong Lensing: Circumventing Assumptions on the Hubble Constant, Sound Horizon, and Dark Energy
School of Physics and Optoelectronic, Yangtze University（长江大学物理与光电工程学院）
Sixty percent of gamma-ray bursts (GRBs) reveal strong MgII absorbing systems, which is a factor of ~2 times the rate seen along lines-of-sight to quasars. The discrepancy in the covering factor is most likely to be the result of either quasars being obscured due to dust, or the consequence of many GRBs being strongly gravitationally lensed. We analyze observations of GRBs that show strong foreground MgII absorption. We Monte-Carlo the distances between foreground galaxies in the HUDF and lines of sight distributed randomly within a radius derived from the covering factor, and find that galaxi…
Strongly gravitationally lensed quasar-galaxy systems allow us to compare competing cosmologies as long as one can be reasonably sure of the mass distribution within the intervening lens. In this paper, we assemble a catalog of 69 such systems, and carry out a one-on-one comparison between the standard model, LCDM, and the R_h=ct Universe. We find that both models account for the lens observations quite well, though the precision of these measurements does not appear to be good enough to favor one model over the other. Part of the reason is the so-called bulge-halo conspiracy that, on average,…
The diffraction-lensing interpretation of GW231123 with astrophysical priors
School of Natural Sciences, Institute for Advanced Study（高等研究院自然科学院）；Center for Gravitational Physics, University of Texas at Austin（德克萨斯大学奥斯汀分校引力物理中心）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；Kavli Institute for Cosmological Physics, The University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Chennai Mathematical Institute（金奈数学研究所）
We report the discovery of 29 promising (and 59 total) new lens candidates from the CFHT Legacy Survey (CFHTLS) based on about 11 million classifications performed by citizen scientists as part of the first Space Warps lens search. The goal of the blind lens search was to identify lens candidates missed by robots (the RingFinder on galaxy scales and ArcFinder on group/cluster scales) which had been previously used to mine the CFHTLS for lenses. We compare some properties of the samples detected by these algorithms to the Space Warps sample and find them to be broadly similar. The image separat…
We present a new model-independent strategy for testing the Friedmann-Lema\^ıtre-Robertson-Walker metric and constraining cosmic curvature, based on future time delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the Distance Sum Rule and determining/cons…
Aims: In this work, we aim to provide a reliable list of gravitational lens (GL) candidates based on a search performed over the entire Gaia Data Release 2 (Gaia DR2). We also show that the sole astrometric and photometric informations coming from the Gaia satellite yield sufficient insights for supervised learning methods to automatically identify GL candidates with an efficiency that is comparable to methods based on image processing. Methods: We simulated 106,623,188 lens systems composed of more than two images, based on a regular grid of parameters characterizing a non-singular isothermal…
Strong gravitational lensing offers a compelling test of the cold dark matter paradigm, as it allows for subhaloes with masses of $\sim10^{9}$ M$_\odot$ and below to be detected. We test commonly-used techniques for detecting subhaloes superposed in images of strongly lensed galaxies. For the lens we take a simulated galaxy in a $\sim10^{13}$ M$_\odot$ halo grown in a high-resolution cosmological hydrodynamical simulation, which we view from two different directions. Though the resolution is high, we note the simulated galaxy still has an artificial core which adds additional complexity to the…
Finding the distribution of matter using lenses - II: deconvolution-based reconstruction with 3x2pt measurements
Korea Astronomy and Space Science Institute（韩国天文学与空间科学研究所）；The Institute of Mathematical Sciences, HBNI（数学科学研究所，HBNI）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；INAF/OAS Bologna, Osservatorio di Astrofisica e Scienza dello Spazio（意大利国家天体物理研究所/博洛尼亚天文台与空间科学观测站）；Department of Physics and Astronomy, Sejong University（世宗大学物理与天文学系）；University of Science and Technology（科学技术大学）
A particular open problem in cosmology is whether dark matter on small scales is clumpy, forming gravitationally-bound halos distributed within the Galaxy. The practical difficulties inherent in testing this hypothesis stem from the fact that, on astrophysical scales, dark matter is solely observable via its gravitational interaction with other objects. This thesis presents a gravitational-lensing-based solution for the mapping and characterisation of low-mass, dark matter halos via their signature in millisecond pulsar observations. This involves: first, determining the time delay and magnifi…
Several semi-analytic models (SAMs) try to explain how galaxies form, evolve and interact inside the dark matter large-scale structure. These SAMs can be tested by comparing their predictions for galaxy-galaxy-galaxy-lensing (G3L), which is weak gravitational lensing around galaxy pairs, with observations. We evaluate the SAMs by Henriques et al. (2015; H15) and by Lagos et al. (2012; L12), implemented in the Millennium Run, by comparing their predictions for G3L to observations at smaller scales than previous studies and also for pairs of lens galaxies from different populations. We compare t…
Newcastle University（纽卡斯尔大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；Carnegie Mellon University（卡内基梅隆大学）；University of California, Berkeley（加州大学伯克利分校）
