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 .