# Constraints on a possible evolution of mass density power-law index in strong gravitational lensing from cosmological data

## TL;DR

This study investigates whether the mass density profile of strong gravitational lensing systems evolves with redshift by analyzing multiple cosmological data sets and considering different parametrizations of the evolution.

## Contribution

It introduces a new method combining SGL, supernovae, and gamma-ray burst data to probe the redshift evolution of the lens mass density profile, considering various parametrizations.

## Key findings

- Results are consistent across different lens redshift sub-samples.
- A mild evolution of the mass density profile is suggested by best-fit parameters.
- The analysis supports a near-constant density profile with slight evolution over redshift.

## 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.