Time Delay Distance Research Articles

Determining Cosmological-model-independent H 0 with Gravitationally Lensed Supernova Refsdal

The reappearance of supernova Refsdal with detailed modeling of the lens cluster allows us to measure the time-delay distance, which serves as a powerful tool to determine the Hubble constant (H 0). We give a cosmological-model-independent method to estimate H 0 through Gaussian process regression, using time-delay measurements from this lensed supernova in combination with supernova data from the Pantheon+ sample. Using eight mass models for the lens cluster, we infer H0=64.2−4.3+4.4kms−1Mpc−1 , and using two cluster models most consistent with the observations, we infer H0=66.3−3.6+3.8kms−1Mpc−1 . Our estimates of the value of H 0 are in 1σ agreement with the results assuming a flat ΛCDM model and the uncertainties are comparable. Our constraint results on H 0 from the eight lens models and the two lens models indicate 2σ and 1.8σ tensions with that estimated by Supernova H0 for the Equation of State, respectively. However, our median values of H 0 from the two sets of lens models show good consistency with H 0 inferred from Planck cosmic microwave background observations assuming a ΛCDM model within 1σ. We also find that our results for H 0 indicate 2σ deviations and 1.7σ deviations from the constraint results of H 0 using six time-delay quasars by H0LiCOW with the same analysis method.

A Model-independent Method to Determine H 0 Using Time-delay Lensing, Quasars, and Type Ia Supernovae

Absolute distances from strong lensing can anchor Type Ia Supernovae (SNe Ia) at cosmological distances giving a model-independent inference of the Hubble constant (H 0). Future observations could provide strong lensing time-delay distances with source redshifts up to z ≃ 4, which are much higher than the maximum redshift of SNe Ia observed so far. In order to make full use of time-delay distances measured at higher redshifts, we use quasars as a complementary cosmic probe to measure cosmological distances at redshifts beyond those of SNe Ia and provide a model-independent method to determine H 0. In this work, we demonstrate a model-independent, joint constraint of SNe Ia, quasars, and time-delay distances from strong lensed quasars. We first generate mock data sets of SNe Ia, quasar, and time-delay distances based on a fiducial cosmological model. Then, we calibrate the quasar parameters model independently using Gaussian process (GP) regression with mock SNe Ia data. Finally, we determine the value of H 0 model-independently using GP regression from mock quasars and time-delay distances from strong lensing systems. As a comparison, we also show the H 0 results obtained from mock SNe Ia in combination with time-delay lensing systems whose redshifts overlap with SNe Ia. Our results show that quasars at higher redshifts show great potential to extend the redshift coverage of SNe Ia and thus enable the full use of strong lens time-delay distance measurements from ongoing cosmic surveys and improve the accuracy of the estimation of H 0 from 2.1% to 1.3% when the uncertainties of the time-delay distances are 5% of the distance values.

TDCOSMO

Time-delay distance measurements of strongly lensed quasars have provided a powerful and independent probe of the current expansion rate of the Universe (H0). However, in light of the discrepancies between early- and late-time cosmological studies, current efforts revolve around the characterisation of systematic uncertainties in the methods. In this work we focus on the mass-sheet degeneracy (MSD), which is commonly considered a significant source of systematics in time-delay strong lensing studies, and aim to assess the constraining power provided by integral field unit (IFU) stellar kinematics. To this end, we approximated the MSD with a cored, two-parameter extension to the adopted lensing mass profiles (with core radius rc and mass-sheet parameter λint), which introduces a full degeneracy between λint and H0 from lensing data alone. In addition, we utilised spatially resolved mock IFU stellar kinematics of time-delay strong lenses, given the prospects of obtaining such high-quality data with the James Webb Space Telescope (JWST) in the near future. We constructed joint strong lensing and generalised two-integral axisymmetric Jeans models, where the time delays, mock imaging, and IFU observations are used as input to constrain the mass profile of lens galaxies at the individual galaxy level and consequently yield joint constraints on the time-delay distance (DΔt) and the angular diameter distance (Dd) to the lens. We find that mock JWST-like stellar kinematics constrain the amount of internal mass sheet that is physically associated with the lens galaxy and limit its contribution to the uncertainties of DΔt and Dd, each at the ≤4% level, without assumptions on the background cosmological model. Incorporating additional uncertainties due to external mass sheets associated with mass structures along the lens line of sight, these distance constraints would translate to a ≲4% precision measurement on H0 in flat Λ cold dark matter cosmology for a single lens. Our study shows that future IFU stellar kinematics of time-delay lenses will be key in lifting the MSD on a per lens basis, assuming reasonable and physically motivated core sizes. However, even in the limit of infinite rc, where DΔt is fully degenerate with λint and is thus not constrained, stellar kinematics of the deflector, time delays, and imaging data will provide powerful constraints on Dd, which becomes the dominant source of information in the cosmological inference.

TDCOSMO

Strong-lensing time delays enable the measurement of the Hubble constant (H0) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H0, effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy Dd = 865−81+85 Mpc and the time-delay distance DΔt = 2180−271+472 Mpc, giving H0 = 77.1−7.1+7.3 km s−1 Mpc−1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system (H0 = 78.3−3.3+3.4 km s−1 Mpc−1) and for seven lenses (H0 = 74.2−1.6+1.6 km s−1 Mpc−1), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us (H0 = 73.3−5.8+5.8 km s−1 Mpc−1). This agreement corroborates the methodology of time-delay cosmography.

Model-independent determination of H0 and ΩK, 0 using time-delay galaxy lenses and gamma-ray bursts

ABSTRACT Combining the ‘time-delay distance’ (DΔt) measurements from galaxy lenses and other distance indicators provides model-independent determinations of the Hubble constant (H0) and spatial curvature (ΩK, 0), only based on the validity of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and geometrical optics. To take the full merit of combining DΔt measurements in constraining H0, we use gamma-ray burst (GRB) distances to extend the redshift coverage of lensing systems much higher than that of Type Ia Supernovae (SNe Ia) and even higher than quasars, whilst the general cosmography with a curvature component is implemented for the GRB distance parametrizations. Combining Lensing + GRB yields $H_0=71.5^{+4.4}_{-3.0}$ km s−1 Mpc−1 and $\Omega _{K,0} = -0.07^{+0.13}_{-0.06}$ (1σ). A flat-universe prior gives slightly an improved $H_0 = 70.9^{+4.2}_{-2.9}$ km s−1Mpc−1. When combining Lensing+GRB + SN Ia, the error bar ΔH0 falls by 25 per cent, whereas ΩK, 0 is not improved due to the degeneracy between SN Ia absolute magnitude, MB, and H0 along with the mismatch between the SN Ia and GRB Hubble diagrams at z ≳ 1.4. Future increment of GRB observations can help to moderately eliminate the MB–H0 degeneracy in SN Ia distances and ameliorate the restrictions on cosmographic parameters along with ΩK, 0 when combining Lensing+SN Ia + GRB. We conclude that there is no evidence of significant deviation from a (an) flat (accelerating) universe and H0 is currently determined at 3 per cent precision. The measurements show great potential to arbitrate the H0 tension between the local distance ladder and cosmic microwave background measurements and provide a relevant consistency test of the FLRW metric.

A New Way to Explore Cosmological Tensions Using Gravitational Waves and Strong Gravitational Lensing

In recent years, a crisis in the standard cosmology has been caused by inconsistencies in the measurements of some key cosmological parameters, the Hubble constant H 0 and cosmic curvature parameter Ω K , for example. It is necessary to remeasure them with the cosmological model-independent methods. In this paper, based on the distance sum rule, we present such a way to constrain H 0 and Ω K simultaneously in the late universe from strong gravitational lensing time-delay (SGLTD) data and gravitational wave (GW) standard siren data simulated from the future observation of the Einstein Telescope (ET). Based on the data for six currently observed SGLTDs, we find that the constraint precision of H 0 from the combined 100 GW events can be comparable with the measurement from the SH0ES collaboration. As the number of GW events increases to 700, the constraint precision of H 0 will exceed that of the Planck 2018 results. Considering 1000 GW events as the conservative estimation of ET in the 10 yr observation, we obtain H 0 = 73.69 ± 0.36 km s−1 Mpc−1 with a 0.5% uncertainty and . In addition, we simulate 55 strong gravitational lensing (SGL) systems with a 6.6% uncertainty for the measurement of time-delay distance. By combining with 1000 GWs, we infer that H 0 = 73.65 ± 0.35 km s−1 Mpc−1 and Ω K = 0.008 ± 0.048. Our results suggest that this approach can play an important role in exploring cosmological tensions.

The determinants of discounting in intergenerational decision-making

We investigate discounting behavior in situations where both intertemporal and social discounting occur simultaneously. Situations of intergenerational conflicts are characterized by both time delay and social distance and can be interpreted either as a combination of current donations with delegated investments for others or of current investments for one's own and future donations to others. Due to well-known self-control problems with respect to investments for one's own, the second interpretation implies overall higher discounting in intergenerational decision problems than the first one. We show experimentally that discounting in intergenerational decision-making indeed lies between the implications of these two interpretations so that self-control problems seem to be at work here as well. This problem can be mitigated by adequate framing supporting the first view of intergenerational decision problems described above. Our findings are relevant for policy makers and researchers alike.

Constraining cosmological parameters from strong lensing with DECIGO and B-DECIGO sources

ABSTRACT 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 hundred 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 redshifts, even with the moderate uncertainties, will set the tight bound on the energy density parameter ΩM for matter, that is, 0.288 ≲ ΩM ≲ 0.314 at best. The constraint on the Hubble constant H0 can be determined using the time delay method. It is found out that at 5σ, |δH0|/H0 ranges from $3{{\ \rm per\ cent}}$ to $11{{\ \rm per\ cent}}$ for DECIGO, and B-DECIGO will give less constrained results, $8{{\ \rm per\ cent}}\ \mathrm{ to}\ 15{{\ \rm per\ cent}}$. In this work, the uncertainties on the luminosity distance and the time delay distance are set to be $10{{\ \rm per\ cent}}$ and $20{{\ \rm per\ cent}}$, respectively. The improvement on measuring these distances will tighten the bounds.

TDCOSMO

Time-delay cosmography with gravitationally lensed quasars plays an important role in anchoring the absolute distance scale and hence measuring the Hubble constant, H0, 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 H0. 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 the measurement of the stellar velocity dispersion of the lensing galaxy, depends on the assumption that the ratio, Ds/Dds, of angular diameter distances to the background quasar and between the lensing galaxy and the quasar can be constrained. This is typically achieved through the assumption of a particular cosmological model. Previous work (TDCOSMO IV) addressed the mass-sheet degeneracy and derived H0 under the assumption of the ΛCDM model. In this paper we show that the mass-sheet degeneracy can be broken without relying on a specific cosmological model by combining lensing with relative distance indicators such as supernovae Type Ia and baryon acoustic oscillations, which constrain the shape of the expansion history and hence Ds/Dds. With this approach, we demonstrate that the mass-sheet degeneracy can be constrained in a cosmological model-independent way. Hence model-independent distance measurements in time-delay cosmography under MSTs can be obtained.

Model-independent Estimation of H 0 and Ω K from Strongly Lensed Fast Radio Bursts

Abstract Model-independent estimation of H 0 and Ω K can provide clues about the origin of the intractable Hubble constant tension and the current cosmic-curvature crisis. Strongly lensed fast radio bursts (FRBs) have been proposed as precision probes of the universe since the time delay ∼  (10 days) between images could be precisely measured due to short durations ∼  ( ms ) of this kind of bright radio pulses. Here, on the basis of the distance sum rule, we investigate the capacity of model-independently estimating these two parameters from time-delay distances of strongly lensed FRBs and luminosity distances of the upcoming Wide Field InfraRed Survey Telescope (WFIRST) type Ia supernovae observations. Considering the expected FRB detection rate of upcoming facilities, we find that H 0 could be determined to a ∼1% precision and Ω K could be constrained to ∼0.1 simultaneously from 10 lensed FRBs. These estimations, which are independent of the energy contents of the universe and validity of Einstein’s equation on cosmological scales, will be complementary to popular probes and of great importance for clarifying the current crises of cosmology.

Watching the formation and reshaping of a Fano resonance in a macroscopic medium

Time-resolved buildup of a Fano resonance in a macroscopic gaseous medium is theoretically studied by attosecond transient absorption spectroscopy. An intense near-infrared field is employed as an adjustable gate to confine the temporal dynamics, enabling one to resolve the line-shape formation in real time. Beyond the region where the single-atom approximation holds, we observe the emergence of spectral spikes with narrow linewidths for certain time delays and propagation distances, which represents that the medium can be delicately structured to be an efficient resonant absorber. Spectral substructures appear on the shoulder of the absorption lines after additional pulse propagation. The links between these features imprinted in spectral profiles and the formation of temporal characteristics in the excitation field are identified. The collective response of the medium versus time delay and propagation distance, in this laser-gated case, provides clues to the time-domain information on autoionization state and the microscopic dynamics occurring at each layer of the medium.

Constraining cosmological and galaxy parameters using strong gravitational lensing systems

Strong gravitational lensing along with the distance sum rule method can constrain both cosmological parameters as well as density profiles of galaxies without assuming any fiducial cosmological model. To constrain galaxy parameters and cosmic curvature $(\Omega_{k0})$, we use the distance ratio data from a recently compiled database of $161$ galactic scale strong lensing systems. We use databases of supernovae type-Ia (Pantheon) and Gamma Ray Bursts (GRBs) for calculating the luminosity distance. To study the model of the lens galaxy, we consider a general lens model namely, the Extended Power-Law model. Further, we take into account two different parametrisations of the mass density power-law index $(\gamma)$ to study the dependence of $\gamma$ on redshift. The best value of $\Omega_{k0}$ suggests a closed universe, though a flat universe is accommodated at $68\%$ confidence level. We find that parametrisations of $\gamma$ have a negligible impact on the best fit value of the cosmic curvature parameter. Furthermore, measurement of time delay can be a promising cosmographic probe via "time delay distance" that includes the ratio of distances between the observer, the lens and the source. We again use the distance sum rule method with time-delay distance dataset of H0LiCOW to put constraints on the Cosmic Distance Duality Relation (CDDR) and the cosmic curvature parameter $(\Omega_{k0})$. For this we consider two different redshift-dependent parametrisations of the distance duality parameter $(\eta)$. The best fit value of $\Omega_{k0}$ clearly indicates an open universe. However, a flat universe can be accommodated at $95\%$ confidence level. Further, at $95\%$ confidence level, no violation of CDDR is observed. We believe that a larger sample of strong gravitational lensing systems is needed in order to improve the constraints on the cosmic curvature and distance duality parameter.

HOLISMOKES

We present the HOLISMOKES programme on strong gravitational lensing of supernovae (SNe) as a probe of SN physics and cosmology. We investigate the effects of microlensing on early-phase SN Ia spectra using four different SN explosion models. We find that distortions of SN Ia spectra due to microlensing are typically negligible within ten rest-frame days after a SN explosion (< 1% distortion within the 1σspread and ≲10% distortion within the 2σspread). This shows the great prospects of using lensed SNe Ia to obtain intrinsic early-phase SN spectra for deciphering SN Ia progenitors. As a demonstration of the usefulness of lensed SNe Ia for cosmology, we simulate a sample of mock lensed SN Ia systems that are expected to have accurate and precise time-delay measurements in the era of theRubinObservatory Legacy Survey of Space and Time (LSST). Adopting realistic yet conservative uncertainties on their time-delay distances and lens angular diameter distances, of 6.6% and 5%, respectively, we find that a sample of 20 lensed SNe Ia would allow us to constrain the Hubble constant (H0) with 1.3% uncertainty in the flat ΛCDM cosmology. We find a similar constraint onH0in an open ΛCDM cosmology, while the constraint degrades to 3% in a flatwCDM cosmology. We anticipate lensed SNe to be an independent and powerful probe of SN physics and cosmology in the upcoming LSST era.

Inverter‐side robust damping controller design of hybrid HVDC with cascaded multi‐infeed MMC converters in asynchronous situation

Objective it is known that the rectifier side control usually suffers from the time delay and long distance communication problems, which could make the damping controller to be invalid and decrease the system stability. Specifically, when the system is in asynchronous operation, the rectifier controllers cannot damp the oscillations in inverter side AC system. Thus, to design the HVDC damping controller at inverter side becomes a feasible solution to avoid these problems. Methods Based on the MMC control strategy, to design the damping controllers at inverter side, the mixed H2/H∞ robust method with regional pole placement is investigated for the two MMC inverters in constant active power control based on the master-slave control mode, where the robustness, control effort and the damping ratios can all be guaranteed simultaneously. During the design process, the simplified system models, namely the TLS-ESPRIT identification algorithm, is also used for controller study. Finally, two robust controllers are obtained based on the proposed method and the inverter side damping controllers are added at the MMCs of hybrid HVDC. Results The damping controllers for hybrid HVDC with cascaded multi-infeed MMCs can be designed at inverter side, which endows the hybrid HVDC with more control functions compared with the classical HVDC systems. The damping controllers can be added at the cascaded multi-infeed MMC inverters in constant active power control, which can enhance the connected AC systems' small stabilities. Conclusions Based on the multi-objective robust theory, the control effectiveness and robustness of the designed controllers can be guaranteed simultaneously, which can damp the low frequency oscillations significantly in different operating situations.

Determining Model-independent H0 and Consistency Tests

Abstract We determine the Hubble constant H 0 precisely (2.3% uncertainty) in a manner independent of the cosmological model through Gaussian process regression, using strong lensing and supernova data. Strong gravitational lensing of a variable source can provide a time-delay distance D Δt and angular diameter distance to the lens D d. These absolute distances can anchor Type Ia supernovae, which give an excellent constraint on the shape of the distance–redshift relation. Updating our previous results to use the H0LiCOW program’s milestone data set consisting of six lenses, four of which have both D Δt and D d measurements, we obtain for a flat universe and for a non-flat universe. We carry out several consistency checks on the data and find no statistically significant tensions, though a noticeable redshift dependence persists in a particular systematic manner that we investigate. Speculating on the possibility that this trend of derived Hubble constant with lens distance is physical, we show how this can arise through modified gravity light propagation, which would also impact the weak lensing σ 8 tension.

Complexity Analysis of Surface Electromyography for Assessing the Myoelectric Manifestation of Muscle Fatigue: A Review.

The surface electromyography (sEMG) records the electrical activity of muscle fibers during contraction: one of its uses is to assess changes taking place within muscles in the course of a fatiguing contraction to provide insights into our understanding of muscle fatigue in training protocols and rehabilitation medicine. Until recently, these myoelectric manifestations of muscle fatigue (MMF) have been assessed essentially by linear sEMG analyses. However, sEMG shows a complex behavior, due to many concurrent factors. Therefore, in the last years, complexity-based methods have been tentatively applied to the sEMG signal to better individuate the MMF onset during sustained contractions. In this review, after describing concisely the traditional linear methods employed to assess MMF we present the complexity methods used for sEMG analysis based on an extensive literature search. We show that some of these indices, like those derived from recurrence plots, from entropy or fractal analysis, can detect MMF efficiently. However, we also show that more work remains to be done to compare the complexity indices in terms of reliability and sensibility; to optimize the choice of embedding dimension, time delay and threshold distance in reconstructing the phase space; and to elucidate the relationship between complexity estimators and the physiologic phenomena underlying the onset of MMF in exercising muscles.

STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408−5354

ABSTRACT We present a blind time-delay cosmographic analysis for the lens system DES J0408−5354. This system is extraordinary for the presence of two sets of multiple images at different redshifts, which provide the opportunity to obtain more information at the cost of increased modelling complexity with respect to previously analysed systems. We perform detailed modelling of the mass distribution for this lens system using three band Hubble Space Telescope imaging. We combine the measured time delays, line-of-sight central velocity dispersion of the deflector, and statistically constrained external convergence with our lens models to estimate two cosmological distances. We measure the ‘effective’ time-delay distance corresponding to the redshifts of the deflector and the lensed quasar $D_{\Delta t}^{\rm eff}=$$3382_{-115}^{+146}$ Mpc and the angular diameter distance to the deflector Dd = $1711_{-280}^{+376}$ Mpc, with covariance between the two distances. From these constraints on the cosmological distances, we infer the Hubble constant H0= $74.2_{-3.0}^{+2.7}$ km s−1 Mpc−1 assuming a flat ΛCDM cosmology and a uniform prior for Ωm as $\Omega _{\rm m} \sim \mathcal {U}(0.05, 0.5)$. This measurement gives the most precise constraint on H0 to date from a single lens. Our measurement is consistent with that obtained from the previous sample of six lenses analysed by the H0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) collaboration. It is also consistent with measurements of H0 based on the local distance ladder, reinforcing the tension with the inference from early Universe probes, for example, with 2.2σ discrepancy from the cosmic microwave background measurement.

MPC-based switched driving model for human vehicle co-piloting considering human factors

In vehicle longitudinal control, improved comfort and reduced operation workload for human drivers are achieved with the ACC (Adaptive Cruise Control), which still requires the driver to maintain full attention on monitoring, meanwhile, the risk of distraction and fatigue rises resulting from the long-term supervising task, which has a strong impact on the successful takeover. The key point to make full use of ACC advantages and make up human’s weakness on supervising task is the reasonable arrangement of control time of ACC and human driver. In this paper, an MPC (Model Predictive Control) based optimized switching strategy of longitudinal driving authority transition is proposed, which aims to provide proper advice for human drivers to handover and takeover control authority, through minimizing the overall index consisted of the operation workload, fuel consumption, takeover risk and tracking errors. In addition, a new driver longitudinal model considering actual reaction time delay and insensitive distance perception of human drivers is proposed as well, which combines with ACC to constitute a typical switched control system called the switched driving model as the predictive model for MPC. The stable condition of the new driver longitudinal model is derived by using describing function method and a sufficient condition to ensure steady switched system is given by using the Lyapunov method and LMI approach. The results of simulator experiments show that the new driver model describes the car-following behavior of real human driver better. What’s more, the simulation results demonstrate that the performance index of switched driving is smaller than the human driving and ACC driving only, and the optimization time is short enough to meet the requirement of engineering practice.

Time-delay cosmographic forecasts with strong lensing and JWST stellar kinematics

ABSTRACT We present a joint strong lensing and stellar dynamical framework for future time-delay cosmography purposes. Based on a pixelated source reconstruction and the axisymmetric Jeans equations, we are capable of constraining cosmological distances and hence the current expansion rate of the Universe (H0) to the few per cent level per lens, when high signal-to-noise integral field unit (IFU) observations from the next generation of telescopes become available. For illustrating the power of this method, we mock up IFU stellar kinematic data of the prominent lens system RXJ1131−1231, given the specifications of the James Webb Space Telescope. Our analysis shows that the time-delay distance (DΔt) can be constrained with 3.1 per cent uncertainty at best, if future IFU stellar kinematics are included in the fit and if the set of candidate model parametrizations contains the true lens potential. These constraints would translate to a 3.2 per cent precision measurement on H0 in flat ΛCDM cosmology from the single lens RXJ1131−1231, and can be expected to yield an H0 measure with ≤2.0 per cent uncertainty, if similar gains in precision can be reached for two additional lens systems. Moreover, the angular diameter distance (Dd) to RXJ1131−1231 can be constrained with 2.4 per cent precision, providing two distance measurements from a single lens system, which is extremely powerful to further constrain the matter density (Ωm). The measurement accuracy of Dd, however, is highly sensitive to any systematics in the measurement of the stellar kinematics. For both distance measurements, we strongly advise to probe a large set of physically motivated lens potentials in the future, to minimize the systematic errors associated with the lens mass parametrization.

Calibrating the standard candles with strong lensing

We propose a new model-independent strategy to calibrate the distance relation in Type Ia supernova (SN) observations and to probe the intrinsic properties of SNe Ia, especially the absolute magnitude M_B, basing on strong lensing observations in the upcoming Large Synoptic Survey Telescope (LSST) era. The strongly lensed quasars can provide the Time Delay Distances (TDD) and the Angular Diameter Distances (ADD) to the lens galaxies. These absolute distance measurements can model-independently anchor the SNe Ia at cosmological distances. We simulated 55 high-quality lensing systems with 5% uncertainties for both TDD and ADD measurements basing on future observation conditions. For the time delay distances and the angular diameter distances as the calibration standards, the calibrated 1sigma uncertainties of M_{B} are approximately 0.24 mag and 0.03 mag, respectively. Besides, we also consider an evolving distance relation, for example, caused by the cosmic opacity. In this case, the 1sigma uncertainties of M_B calibrated with TDD and ADD are approximately 0.31 mag and 0.06 mag, respectively. The results show that the ADD method will be a promising tool for calibrating supernovae.