A Distance-deviation Consistency and Model-independent Method to Test the Cosmic Distance–Duality Relation

A distance-deviation consistency and model-independent method to test the cosmic distance duality relation (CDDR) is provided. The worth attention on two aspects: firstly, a used pair subsamples: instead of pairing subsamples with redshift deviation smaller than \textbf{value}, say $\left\vert \Delta z\right\vert <0.005$. between decreases ensure stays same. selects more at high redshift, up $z=2.16$, provides 120 subsample pairs. Secondly, involves latest data set $1048$ type Ia supernovae (SNe Ia) $205$ strong gravitational lensing systems (SGLS), which are obtain luminosity distances $D_L$ ratio angular diameter $D_A$ respectively. With method, parameters CDDR, SNe light-curve, SGLS fitted simultaneously. \textbf{The result shows} that $\eta = 0.047^{+0.190}_{-0.151}$ CDDR validated 1$\sigma$ confidence level for form $\frac{{{D_L}}}{{{D_A}}}{(1 + z)^{ - 2}} =1+ \eta z$.