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 $\mathbf{\text{value}}$, say $\mid \mathrm{\Delta }z\mid <0.005$. 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. $\mathbf{\text{The}}\mathbf{\text{result}}\mathbf{\text{shows}}$ that $\eta =0.047_{-0.151}^{+0.190}$ and CDDR is validated at 1$\sigma$ confidence level for the form $\frac{D_L}{D_A}(1+z{)}^{-2}=1+\eta z$.