The distance sum rule from strong lensing systems and quasars - test of cosmic curvature and beyond

Testing the distance-sum-rule in strong lensing systems provides an interesting method to determine the curvature parameter $\Omega_k$ using more local objects. In this paper, we apply this method to a quite recent data set of strong lensing systems in combination with intermediate-luminosity quasars calibrated as standard rulers. In the framework of three types of lens models extensively used in strong lensing studies (SIS model, power-law spherical model, and extended power-law lens model), we show that the assumed lens model has a considerable impact on the cosmic curvature constraint, which is found to be compatible or marginally compatible with the flat case (depending on the lens model adopted). Analysis of low, intermediate and high-mass sub-samples defined according to the lens velocity dispersion demonstrates that, although it is not reasonable to characterize all lenses with a uniform model, such division has little impact on cosmic curvature inferred. Finally, thinking about future when massive surveys will provide their yields, we simulated a mock catalog of strong lensing systems expected to be seen by the LSST, together with a realistic catalog of quasars. We found that with about 16000 such systems, combined with the distance information provided by 500 compact milliarcsecond radio sources seen in future radio astronomical surveys, one would be able to constrain the cosmic curvature with an accuracy of $\Delta \Omega_k\simeq 10^{-3}$, which is comparable to the precision of \textit{Planck} 2015 results.