A Consistent Test of the Distance-Duality Relation with Galaxy Clusters and Type Ia Supernave

TL;DR

This paper introduces a new cosmology-independent method to test the distance-duality relation using galaxy clusters and Type Ia supernovae, ensuring redshift matching to improve accuracy.

Contribution

It presents a novel approach that interpolates supernova luminosity distances at galaxy cluster redshifts, reducing bias and providing more stringent tests of the distance-duality relation.

Findings

The relation η ≡ D_L/(D_A (1+z)^2) holds within 2σ confidence level.

The method improves upon previous tests by accounting for redshift bias.

Results support the validity of the distance-duality relation in the examined data.

Abstract

We propose a new consistent method to test of the distance-duality (DD) relation which related angular diameter distances (DA) to the luminosity distances (DL) in a cosmology-independent way. In order to avoid any bias brought by redshift incoincidence between galaxy clusters and Type Ia Supernave (SNe Ia), as well as to ensure the integrity of the galaxy clusters samples, we obtain the luminosity distance of a certain SN Ia point at the same redshift of the corresponding galaxy cluster by interpolating from the nearby SNe Ia. With the observational data at the same redshifts of the angular diameter distances from the complete 38 galaxy cluster sample for the spherical model and the corrected luminosity distances interpolated from the Union2 set, we find that $\eta \equiv {D_L}{(1+z)}^{-2}/{D_A}=1$ is satisfied within $2\sigma$ confidence level for various parameterizations of $\eta(z)$, which are more stringent than previous testing results without considering redshift bias.