Title: Constraints on a possible evolution of mass density power-law index in strong gravitational lensing from cosmological data,
Abstract: 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.