A Distance-Deviation Consistency and Model-Independent Method to Test the Cosmic Distance-Duality Relation

TL;DR

This paper introduces a novel, model-independent method to test the cosmic distance duality relation using paired subsamples with minimal redshift deviation, leveraging extensive supernova and gravitational lensing data, and confirms the relation within 1σ confidence.

Contribution

It proposes a new distance-deviation consistency approach for pairing subsamples and applies a model-independent analysis to validate the CDDR with large datasets.

Findings

CDDR is validated at 1σ confidence level.

120 subsample pairs used up to redshift 2.16.

Parameters of CDDR and related data fitted simultaneously.

Abstract

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 $\frac{{{D_L}}}{{{D_A}}}{(1 + z)^{ - 2}} =1+ \eta z$.