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.
