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