Constraints on a possible evolution of mass density power-law index in
  strong gravitational lensing from cosmological data
  In this work, by using strong gravitational lensing (SGL) observations along
with Type Ia Supernovae (Union2.1) and gamma ray burst data (GRBs), we propose
a new method to study a possible redshift evolution of $\gamma(z)$, the mass
density power-law index of strong gravitational lensing systems. In this
analysis, we assume the validity of cosmic distance duality relation and the
flat universe. In order to explore the $\gamma(z)$ behavior, three different
parametrizations are considered, namely: (P1) $\gamma(z_l)=\gamma_0+\gamma_1
z_l$, (P2) $\gamma(z_l)=\gamma_0+\gamma_1 z_l/(1+z_l)$ and (P3)
$\gamma(z_l)=\gamma_0+\gamma_1 \ln(1+z_l)$, where $z_l$ corresponds to lens
redshift. If $\gamma_0=2$ and $\gamma_1=0$ the singular isothermal sphere model
is recovered. Our method is performed on SGL sub-samples defined by different
lens redshifts and velocity dispersions. For the former case, the results are
in full agreement with each other, while a 1$\sigma$ tension between the
sub-samples with low ($\leq 250$ km/s) and high ($>250$ km/s) velocity
dispersions was obtained on the ($\gamma_0$-$\gamma_1$) plane. By considering
the complete SGL sample, we obtain $\gamma_0 \approx 2$ and $ \gamma_1 \approx
0$ within 1$\sigma$ c.l. for all $\gamma(z)$ parametrizations. However, we find
the following best fit values of $\gamma_1$: $-0.085$, $-0.16$ and $-0.12$ for
P1, P2 and P3 parametrizations, respectively, suggesting a mild evolution for
$\gamma(z)$. By repeating the analysis with Type Ia Supernovae from JLA
compilation, GRBs and SGL systems this mild evolution is reinforced.
