Cosmological test using strong gravitational lensing systems
  As one of the probes of universe, strong gravitational lensing systems allow
us to compare different cosmological models and constrain vital cosmological
parameters. This purpose can be reached from the dynamic and geometry
properties of strong gravitational lensing systems, for instance, time-delay
$\Delta\tau$ of images, the velocity dispersion $\sigma$ of the lensing
galaxies and the combination of these two effects, $\Delta\tau/\sigma^2$. In
this paper, in order to carry out one-on-one comparisons between $\Lambda$CDM
universe and $R_h=ct$ universe, we use a sample containing 36 strong lensing
systems with the measurement of velocity dispersion from the SLACS and LSD
survey. Concerning the time-delay effect, 12 two-image lensing systems with
$\Delta\tau$ are also used. In addition, Monte Carlo (MC) simulations are used
to compare the efficiency of the three methods as mentioned above. From
simulations, we estimate the number of lenses required to rule out one model at
the $99.7\%$ confidence level. Comparing with constraints from $\Delta\tau$ and
the velocity dispersion $\sigma$, we find that using $\Delta\tau/\sigma^2$ can
improve the discrimination between cosmological models. Despite the
independence tests of these methods reveal a correlation between
$\Delta\tau/\sigma^2$ and $\sigma$, $\Delta\tau/\sigma^2$ could be considered
as an improved method of $\sigma$ if more data samples are available.
