On the cosmic distance duality relation and the strong gravitational lens power law density profile

Many new strong gravitational lensing (SGL) systems have been discovered in the last two decades with the advent of powerful new space and ground-based telescopes. The effect of the lens mass model (usually the power-law mass model) on cosmological parameters constraints has been performed recently in literature. In this paper, by using SGL systems and Supernovae type Ia observations, we explore if the power-law mass density profile ($\rho \propto r^{-\gamma}$) is consistent with the cosmic distance duality relation (CDDR), $D_L(1+z)^{-2}/D_A=\eta(z)=1$, by considering different lens mass intervals. { It has been obtained that the verification of the CDDR validity is significantly dependent on lens mass interval considered: the sub-sample with $\sigma_{ap} \geq 300$ km/s (where $\sigma_{ap}$ is the lens apparent stellar velocity dispersion) is in full agreement with the CDDR validity, the sub-sample with intermediate $\sigma_{ap}$ values ($200 \leq \sigma_{ap} < 300)$ km/s is marginally consistent with $\eta=1$ and, finally, the sub-sample with low $\sigma_{ap}$ values ($\sigma_{ap} < 200$ km/s) ruled out the CDDR validity with high statistical confidence. Therefore, if one takes the CDDR as guarantee, our results suggest that using a single density profile is not suitable to describe lens with low $\sigma_{ap}$ values and it is only an approximate description to lenses with intermediate mass interval. }