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 γ(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 γ(z) behaviour, three different parametrizations are considered, namely: (P1) γ(zl) = γ0 + γ1zl; (P2) γ(zl) = γ0 + γ1zl/(1 + zl); and (P3) γ(zl) = γ0 + γ1ln (1 + zl), where zl corresponds to lens redshift. If γ0 = 2 and γ1 = 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 1s tension between the sub-samples with low (≤250 km s-1) and high (> 250 km s-1) velocity dispersions was obtained on the (γ0-γ1) plane. By considering the complete SGL sample, we obtain γ0 ≈ 2 and γ1 ≈ 0 within 1s c.l. for all γ(z) parametrizations. However, we find the following best-fitting values of γ1: -0.085; -0.16; and -0.12 for P1, P2 and P3 parametrizations, respectively, suggesting a mild evolution for γ(z). By repeating the analysis with Type Ia Supernovae from Joint Light Analysis compilation, GRBs and SGL systems this mild evolution is reinforced.