Constraints on cosmological models from strong gravitational lensing
  systems
  Strong lensing has developed into an important astrophysical tool for probing
both cosmology and galaxies (their structure, formation, and evolution). Using
the gravitational lensing theory and cluster mass distribution model, we try to
collect a relatively complete observational data concerning the Hubble constant
independent ratio between two angular diameter distances $D_{ds}/D_s$ from
various large systematic gravitational lens surveys and lensing by galaxy
clusters combined with X-ray observations, and check the possibility to use it
in the future as complementary to other cosmological probes. On one hand,
strongly gravitationally lensed quasar-galaxy systems create such a new
opportunity by combining stellar kinematics (central velocity dispersion
measurements) with lensing geometry (Einstein radius determination from
position of images). We apply such a method to a combined gravitational lens
data set including 70 data points from Sloan Lens ACS (SLACS) and Lens
Structure and Dynamics survey (LSD). On the other hand, a new sample of 10
lensing galaxy clusters with redshifts ranging from 0.1 to 0.6 carefully
selected from strong gravitational lensing systems with both X-ray satellite
observations and optical giant luminous arcs, is also used to constrain three
dark energy models ($\Lambda$CDM, constant $w$ and CPL) under a flat universe
assumption. For the full sample ($n=80$) and the restricted sample ($n=46$)
including 36 two-image lenses and 10 strong lensing arcs, we obtain relatively
good fitting values of basic cosmological parameters, which generally agree
with the results already known in the literature. This results encourages
further development of this method and its use on larger samples obtained in
the future.
