# No evidence for the evolution of mass density power-law index $\gamma$ from strong gravitational lensing observation

## TL;DR

This study uses strong gravitational lensing data to test if the mass density profile index $\\gamma$ evolves over cosmic time, finding no evidence for such evolution and showing the constraint is independent of the cosmological model.

## Contribution

It provides the first comprehensive analysis indicating that the mass density power-law index \(\gamma\) does not evolve with redshift, regardless of the cosmological model assumptions.

## Key findings

- No evidence for evolution of \(\gamma\) from SGL data.
- Constraint on \(\gamma\) is independent of the cosmological model.
- SGL observations primarily determine \(\gamma\) constraints.

## Abstract

In this paper, we consider the singular isothermal sphere lensing model that has a spherically symmetric power-law mass distribution $\rho_{tot}(r)\sim r^{-\gamma}$. We investigate whether the mass density power-law index $\gamma$ is cosmologically evolutionary by using the strong gravitational lensing (SGL) observation, in combination with other cosmological observations. We also check whether the constraint result of $\gamma$ is affected by the cosmological model, by considering several simple dynamical dark energy models. We find that the constraint on $\gamma$ is mainly decided by the SGL observation and independent of the cosmological model, and we find no evidence for the evolution of $\gamma$ from the SGL observation.