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

Abstract: 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. }