Strong lensing time delay measurements provide a valuable and almost model-independent tool for cosmological investigations. In this work we recognize that they also carry information on the strength of the gravitational coupling at the redshift of the lens, and thus could be in principle used to test the equivalence principle on extragalactic scales. For the case of an extended lens with a static mass distribution we explicitly derive an analytical relation between $\dot{G}/G$ and the relative variation of the time delay. For illustrative purpose, we apply our formula to the light curves of multiple images of the quasar DES J0408-5354 and simulated ones, which results in weak constraints on the variation of $\dot{G}/G$ of order $10^{-1}-10^{-2} \, yr^{-1}$ in the best scenario. Finally, we briefly discuss how those constraints can be improved in the next future.
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…
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…
In this paper we investigate the relation between the potential and geometric time delays in gravitational lensing. In the original paper of Shapiro (1964), it is stated that there is a time delay in the radar signals between Earth and Venus that pass near a massive object (the Sun), compared to the path taken in the absence of any mass. The reason for this delay is connected with the influence of gravity on the coordinate velocity of a light ray in a gravitational potential. The contribution from the change of the path length, which happens to be of second order, is considered as negligible. …
We show in detail that the recently derived expression for evaluating the integrated Sachs-Wolfe (ISW) temperature shift in the cosmic microwave background (CMB) caused by individual embedded (compensated) lenses is equivalent to the conventional approach for flat background cosmologies. The conventional approach requires evaluating an integral of the time derivative of the lensing potential, whereas the new Fermat potential approach is simpler and only requires taking a derivative of the potential part of the time delay.
Gravitational lensing has long been used to measure or constrain cosmology models. Although the lensing effect of gravitational waves has not been observed by LIGO/Virgo, it is expected that there can be a few to a few hundreds lensed events to be detected by the future Japanese space-borne interferometers DECIGO and B-DECIGO, if they are running for 4 years. Given the predicted lensed gravitational wave events, one can estimate the constraints on the cosmological parameters via the lensing statistics and the time delay methods. With the lensing statistics method, the knowledge of the lens red…
An intervening galaxy acts as a gravitational lens and produces multiple images of a single source such as a remote galaxy. Galaxies have peculiar speeds in addition to the bulk motion arising due to the expansion of the universe. There is a difference in light arrival times between lensed images. We calculate more realistic time delays between lensed images when galaxy peculiar motions, that is the motion of the Lens, the Source and the Observer are taken into consideration neglecting the gravitomagnetic effects.
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…
We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom as the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to the arbitrary angles of the standard one, which is valid at small a…
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…
Context. Time delay lensing is a powerful tool to measure the Hubble constant $H_0$. In order to obtain an accurate estimate of $H_0$ from a sample of time delay strong lenses, however, it is necessary to have a very good knowledge of the mass structure of the lens galaxies. Strong lensing data on their own are not sufficient to break the degeneracy between $H_0$ and the lens model parameters, on a single object basis. Aims. The goal of this study is to determine whether it is possible to break the $H_0$-lens structure degeneracy with the statistical combination of a large sample of time-delay…
We derive stringent constraints on neutrino speed, weak equivalence principle violation, Lorentz invariance violation, and dual lensing from the first high-energy astrophysical neutrino source: TXS 0506+056. Observation of neutrino (IceCube-170922A) and photons in a similar time frame and from the same direction is used to derive these limits. We describe ways in which these constraints can be further improved by orders of magnitude.
We have built a new model for the lens system SDSS J1004+4112 including the recently measured time delay of the fourth quasar image. This time delay has a strong influence on the inner mass distribution of the lensing cluster ($ρ\propto r^{-α}$) allowing us to determine $α=1.18^{+0.02(+0.11)}_{-0.03(-0.18)}$ at the 68% (95%) confidence level in agreement with hydrodynamical simulations of massive galaxy clusters. We find an offset between the brightest cluster galaxy (BCG) and the dark matter halo of $3.8^{+0.6(+1.4)}_{-0.7(-1.3)}$ kpc at 68% (95%) confidence which is compatible with other gal…
Time delay in Schwarzschild spacetime for null and timelike signals with arbitrary velocity $v$ is studied. The total travel time $t_\mathrm{if}$ is evaluated both exactly and approximately in the weak field limit, with the result given as functions of signal velocity, source-lens and lens-observer distances, angular position of the source and lens mass. Two time delays, $Δt_v$ between signals with different velocities but coming from same side of the lens and $Δt_\mathrm{p}$ between signals from different sides of the lens, as well as the difference $Δt_{\mathrm{p}v}$ between two $Δt_\mathrm{…
Multiply imaged time-variable sources can be used to measure absolute distances as a function of redshifts and thus determine cosmological parameters, chiefly the Hubble Constant H$_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 …
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…
One application of the Cosmological Gravitational Lensing in General Relativity is the measurement of the Hubble constant H_0 using the time delay Delta t between multiple images of lensed quasars. This method has already been applied, obtaining a value of H_0 compatible with that obtained from the SNe 1A, but non compatible with that obtained studying the anisotropies of the CMB. This difference could be a statistical fluctuation or an indication of new physics beyond the Standard Model of Cosmology, so it desirable to improve the precision of the measurements. At the current technological ca…
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…
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）
Testing $f(Q)$ Gravity with DESI DR2 and Strong-Lensing Time Delays
Henan Academy of Sciences（河南省科学院）；GLA University（GLA大学）；University of Delhi（德里大学）；Symbiosis International (Deemed University)（西姆比奥西斯国际（认定）大学）；Qingdao University of Science and Technology（青岛科技大学）
Recently, the LIGO-Virgo Collaboration (LVC) concluded that there is no evidence for lensed gravitational waves (GW) in the first half of the O3 run, claiming "We find the observation of lensed events to be unlikely, with the fractional rate at $μ>2$ being $3.3\times 10^{-4}$". While we agree that the chance of an individual GW event being lensed at $μ>2$ is smaller than $10^{-3}$, the number of observed events depends on the product of this small probability times the rate of mergers at high redshift. Observational constraints from the stochastic GW background indicate that the rate of conven…
Assuming the $Λ$CDM model, the CMB and BAO observations indicate a very flat Universe. Model-independent measurements are therefore worth studying. Time delays measured in lensed quasars provide the time delay distances. When compared with the luminosity distances from Supernova Ia observation, the measurements can provide the curvature information under the Distance Sum Rule of FLRW metric. This method is limited by the low redshifts of SNe Ia. In this work, we propose gravitational waves from the Einstein Telescope as standard sirens which reach higher redshifts covering the redshift range o…
We present a novel test of general relativity (GR): measuring the geometric component of the time delay due to gravitational lensing. GR predicts that photons and gravitational waves follow the same geodesic paths and thus experience the same geometric time delay. We show that for typical systems, the time delays are tens of seconds, and thus can dominate over astrophysical delays in the timing of photon emission. For the case of GW 170817, we use a multi-plane lensing code to evaluate the time delay due to four massive halos along the line of sight. From literature mass and distance measureme…
Measurements of The Hubble-Lemaitre constant from early- and local-universe observations show a significant discrepancy. In an attempt to understand the origin of this mismatch, independent techniques to measure H0 are required. One such technique, strong lensing time delays, is set to become a leading contender amongst the myriad methods due to forthcoming large strong lens samples. It is therefore critical to understand the systematic effects inherent in this method. In this paper, we quantify the influence of additional structures along the line-of-sight by adopting realistic light cones de…
Measurements of time delays between multiple quasar images produced by strong lensing are reaching a sensitivity that makes them a promising cosmological probe. Future surveys will provide significantly more measurements, reaching unprecedented depth in redshift, making strong lensing time delay (SLTD) observations competitive with other background probes. We forecast constraints on the nature of dark energy from upcoming SLTD surveys, simulating future catalogues with different numbers of lenses distributed up to redshift $z\sim 1$ and focusing on cosmological parameters such as the Hubble co…
We present new light curves for the four bright images of the five image cluster-lensed quasar gravitational lens system SDSS~J1004+4112. The light curves span 14.5 yr and allow measurement of the time delay between the trailing bright quasar image D and the leading image C. When we fit all four light curves simultaneously and combine the models using the Bayes information criterion, we find a time delay of $Δt_{DC}= 2458.47 \pm 1.02$ days (6.73 yr), the longest ever measured for a gravitational lens. For the other two independent time delays we obtain $Δt_{BC}=782.20 \pm 0.43$ days (2.14 yr) …
There is a persistent $H_0$-tension, now at more than $\gtrsim 4σ$ level, between the local distance ladder value and the \emph{Planck} cosmic microwave background measurement, in the context of flat $Λ$CDM model. We reconstruct $H(z)$ in a cosmological-model-independent way using three low-redshift distance probes including the latest data from baryon acoustic oscillation, Type Ia supernova and four gravitational lensing Time-Delay observations. We adopt general parametric models of $H(z)$ and assume a Gaussian prior on the sound horizon at drag epoch, $r_{\mathrm s}$, from \emph{Planck} meas…
Accelerating black holes, connected to cosmic strings could evolve to supermassive black holes. However, if they are going to take part in structure formation and resides at the center of galaxies, their acceleration should be small. This slow acceleration does not change the shadow or image position in gravitational lensing effect significantly. However we show that the time delay associated to these images change significantly. This is in contrast with when the theory governing the strong gravitational field around the black hole is different from general relativity, where not only the diffe…
The time delay measured between the images of gravitationally lensed quasars probes a combination of the angular diameter distance to the source-lens system and the mass density profile of the lens. Observational campaigns to measure such systems have reported a determination of the Hubble parameter H0 that shows significant tension with independent determination based on the cosmic microwave background (CMB) and large scale structure (LSS). We show that lens mass models that exhibit a cored component, coexisting with a cusp, probe a degenerate direction in the lens model parameter space, bein…
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 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 …
The expected event rate of lensed gravitational wave sources scales with the merger rate at redshift $z\geq 1$, where the optical depth for lensing is high. It is commonly assumed that the merger rate of the astrophysical compact objects is closely connected with the star formation rate, which peaks around redshift $z\sim 2$. However, a major source of uncertainty is the delay time between the formation and merger of compact objects. We explore the impact of delay time on the lensing event rate. We show that as the delay time increases, the peak of the merger rate of gravitational wave sources…
Strongly lensed quasars with time-delay measurements are well known to provide the "time-delay distances" $D_{Δt}=(1+z_L)D_LD_S/D_{LS}$ and the angular diameter distances to lens galaxies $D_L$. These two kinds of distances give stringent constraints on cosmological parameters. In this work, we explore a different use of time-delay observables: Under the assumption of a flat Universe, strong lensing observations can accurately measure the angular diameter distances to sources $D_S$. The corresponding redshifts of quasars may be up to $z_S\sim4$ according to the forecast. The high-redshift dist…
