Testing the Distance-Duality Relation with a Combination of Cosmological Distance Observations

TL;DR

This paper tests the distance-duality relation using combined supernova and galaxy cluster data, finding it holds within 1σ confidence level and highlighting the importance of redshift matching in such analyses.

Contribution

It introduces a method to accurately test the distance-duality relation by carefully selecting data points to minimize redshift mismatch and considers multiple parameterizations of the relation.

Findings

No significant deviation from the distance-duality relation within 1σ confidence level.

Redshift matching criteria significantly affect the test results.

The relation is well satisfied across various parameterizations.

Abstract

In this paper, we propose an accurate test of the distance-duality (DD) relation, $\eta=D_{L}(z)(1+z)^{-2}/D_{A}(z)=1$ (where $D_{L}$ and $D_{A}$ are the luminosity distances and angular diameter distances, respectively), with a combination of cosmological observational data of Type Ia Supernave (SNe Ia) from Union2 set and the galaxy cluster sample under an assumption of spherical model. In order to avoid bias brought by redshift incoincidence between observational data and to consider redshift error bars of both clusters and SNe Ia in analysis, we carefully choose the SNe Ia points which have the minimum acceptable redshift difference of the galaxy cluster sample ($|\Delta z|_{\rm min} =\sigma_{z, \rm SN}+\sigma_{z, \rm cluster}$). By assuming $\eta$ a constant and functions of the redshift parameterized by six different expressions, we find that there exists no conceivable evidence for variations in the DD relation concerning with observational data, since it is well satisfied within $1\sigma$ confidence level for most cases. Further considering different values of $\Delta z$ in constraining, we also find that the choosing of $\Delta z$ may play an important role in this model-independent test of the distance-duality relation for the spherical sample of galaxy clusters.