Strongly Lensed Transient Sources:A Review

The past decades have witnessed a lot of progress in gravitational lensing with two main targets:stars and galaxies(with active galactic nuclei).The success is partially attributed to the continuous luminescence of these sources making the detection and monitoring relatively easy.With the running of ongoing and upcoming large facilities/surveys in various electromagnetic and gravitational-wave bands,the era of time-domain surveys would guarantee constant detection of strongly lensed explosive transient events,for example,supernovae in all types,gamma ray bursts with afterglows in all bands,fast radio bursts,and even gravitational waves.Lensed transients have many advantages over the traditional targets in studying the Universe,and magnification effect helps to understand the transients themselves at high redshifts.In this review article,on base of the recent achievements in literature,we summarize the methods of searching for different kinds of lensed transient signals,the latest results on detection and their applications in fundamental physics,astrophysics,and cosmology.At the same time,we give supplementary comments as well as prospects of this emerging research direction that may help readers who are interested in entering this field.

What do parameterized Om(z) diagnostics tell us in light of recent observations?

In this paper, we propose a new parametrization for Om(z) diagnostics and show how the most recent and significantly improved observations concerning the H(z) and SN Ia measurements can be used to probe the consistency or tension between the ΛCDM model and observations. Our results demonstrate that H0 plays a very important role in the consistency test of ΛCDM with H(z)data. Adopting the Hubble constant priors from Planck 2013 and Riess, one finds considerable tension between the current H(z) data and ΛCDM model and confirms the conclusions obtained previously by others. However, with the Hubble constant prior taken from WMAP9, the discrepancy between H(z) data and ΛCDM disappears, i.e., the current H(z) observations still support the cosmological constant scenario. This conclusion is also supported by the results derived from the Joint Lightcurve Analysis(JLA) SN Ia sample. The best-fit Hubble constant from the combination of H(z)+JLA(H00 = 68.81+1.5-1.49 km s-1 Mpc-1) is very consistent with results derived both by Planck 2013 and WMAP9, but is significantly different from the recent local measurement by Riess.

Comparison of cosmological models using standard rulers and candles

In this paper, we used standard rulers and standard candles （separately and jointly） to explore five popular dark energy models under the assumption of the spatial flatness of the Universe. As standard rulers, we used a data set comprised of 118 galactic scale strong lensing systems （individual standard rulers if properly calibrated for the mass density profile） combined with BAO diagnostics （statistical standard ruler）. Type Ia supernovae served as standard candles. Unlike most previous statistical studies involving strong lensing systems, we relaxed the assumption of a singular isothermal sphere （SIS） in favor of its generalization： the power-law mass density profile. Therefore, along with cosmological model parameters, we fitted the power law index and its first derivative with respect to the redshift （thus allowing for mass density profile evolution）. It turned out that the best fitted ~/parameters are in agreement with each other, irrespective of the cosmological model considered. This demonstrates that galactic strong lensing systems may provide a complementary probe to test the properties of dark energy. The fits for cosmological model parameters which we obtained are in agreement with alternative studies performed by other researchers. Because standard rulers and standard candles have different parameter degeneracies, a combination of stan- dard rulers and standard candles gives much more restrictive results for cosmological parameters. Finally, we attempted an analysis based on model selection using information theoretic criteria （AIC and BIC）. Our results support the claim that the cosmological constant model is still best and there is no （at least statistical） reason to prefer any other more complex model.

Dark energy constraints from joint analysis of standard rulers and standard candles

We performed joint analysis of five cosmological models invoked to explain the accelerating expansion of the Universe.We used the data from strong gravitational lensing systems,locations of cosmic microwave background acoustic peaks and baryon acoustic oscillation data in combination with supernova Ia data（Union2 compilation）.The observables we used came from both standard rulers and standard candles,so they had different parameter degeneracies and different restrictive powers in the parameter spaces of cosmological models.The best fits we obtained for the model parameters in joint analysis turned out to prefer cases effectively equivalent to the ΛCDM model.They were also in agreement with other combined studies performed by other authors on different sets of diagnostic probes.Information theoretic methods used to assess which model is most supported by the data lead to the conclusion that the concordance model ΛCDM is clearly preferred in joint analysis.The quintessence（both having constant or time varying equation of state） and Chaplygin gas get considerably less support from the data while the brane world（DGP） scenario is practically ruled out.

Multiple measurements of quasars acting as standard probes: Model independent calibration and exploring the dark energy equation of states

Recently, two classes of quasar samples were identified, which are promising as new cosmological probes extending to higher redshifts. The first sample uses the nonlinear relation between the ultraviolet and X-ray luminosities of quasars to derive luminosity distances, whereas the linear sizes of compact radio quasars in the second sample can serve as standardized rulers, providing angular-diameter distances. In this study, under the assumption of a flat universe, we refreshed the calibration of multiple measurements of high-redshift quasars(in the framework of a cosmological-model-independent method with the newest Hubble parameters data). Furthermore, we placed constraints on four models that characterize the cosmic equation of state(w). The obtained results show that:(1) the two quasar samples could provide promising complementary probes at much higher redshifts,whereas compact radio quasars perform better than ultraviolet and X-ray quasars at the current observational level;(2) strong degeneracy between the cosmic equation of state(w) and Hubble constant(H0) is revealed, which highlights the importance of independent determination of H0 from time-delay measurements of strongly lensed quasars;(3) together with other standard ruler probes, such as baryon acoustic oscillation distance measurements, the combined QSO+BAO measurements are consistent with the standard ΛCDM model at a constant equation of state w =-1;(4) ranking the cosmological models, the polynomial parametrization gives a rather good fit among the four cosmic-equation-of-state models, whereas the Jassal-Bagla-Padmanabhan(JBP) parametrization is substantially penalized by the Akaike Information Criterion and Bayesian Information Criterion.