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 (ρ ∝ r-γ) is consistent with the cosmic distance duality relation (CDDR), DL (1+z)-2/DA = η(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 σap ≥ 300 km/s (where σap is the lens apparent stellar velocity dispersion) is in full agreement with the CDDR validity, the sub-sample with intermediate σap values (200 ≤ σap < 300) km/s is marginally consistent with η = 1 and, finally, the sub-sample with low σap values (σap < 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 σap values and it is only an approximate description to lenses with intermediate mass interval.
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