Cosmology with Strong Lensing Systems
  In this paper, we assemble a catalog of 118 strong gravitational lensing
systems from SLACS, BELLS, LSD and SL2S surveys and use them to constrain the
cosmic equation of state. In particular we consider two cases of dark energy
phenomenology: $XCDM$ model where dark energy is modeled by a fluid with
constant $w$ equation of state parameter and in Chevalier - Polarski - Linder
(CPL) parametrization where $w$ is allowed to evolve with redshift: $w(z) = w_0
+ w_1 \frac{z}{1+z}$. We assume spherically symmetric mass distribution in
lensing galaxies, but relax the rigid assumption of SIS model in favor to more
general power-law index $\gamma$, also allowing it to evolve with redshifts
$\gamma(z)$. Our results for the $XCDM$ cosmology show the agreement with
values (concerning both $w$ and $\gamma$ parameters) obtained by other authors.
We go further and constrain the CPL parameters jointly with $\gamma(z)$. The
resulting confidence regions for the parameters are much better than those
obtained with a similar method in the past. They are also showing a trend of
being complementary to the supernova Ia data. Our analysis demonstrates that
strong gravitational lensing systems can be used to probe cosmological
parameters like the cosmic equation of state for dark energy. Moreover, they
have a potential to judge whether the cosmic equation of state evolved with
time or not.
