Cosmological-model-independent tests for the distance-duality relation from Galaxy Clusters and Type Ia Supernova

TL;DR

This study tests the distance-duality relation using galaxy cluster and supernova data without assuming a specific cosmological model, finding it consistent with observations within certain confidence levels.

Contribution

It provides a model-independent verification of the distance-duality relation using multiple parameterizations and observational datasets.

Findings

DD relation compatible with data at 1σ for De Filippis sample

DD relation compatible at 3σ for Bonamente sample

Results support the validity of the DD relation with current observations

Abstract

We perform a cosmological-model-independent test for the distance-duality (DD) relation $\eta(z)=D_L(z)(1+z)^{-2}/D_A(z)$, where $D_L$ and $D_A$ are the luminosity distance and angular diameter distance respectively, with a combination of observational data for $D_L$ taken from the latest Union2 SNe Ia and that for $D_A$ provided by two galaxy clusters samples compiled by De Filippis {\it et al.} and Bonamente {\it et al.}. Two parameterizations for $\eta(z)$, i.e., $\eta(z)=1+\eta_0z$ and $\eta(z)=1+\eta_0z/(1+z)$, are used. We find that the DD relation can be accommodated at $1\sigma$ confidence level (CL) for the De Filippis {\it et al.} sample and at $3\sigma$ CL for the Bonamente {\it et al.} sample. We also examine the DD relation by postulating two more general parameterizations: $\eta(z)=\eta_0+\eta_1z$ and $\eta(z)=\eta_0+\eta_1z/(1+z)$, and find that the DD relation is compatible with the results from the De Filippis {\it et al.} and the Bonamente {\it et al.} samples at $1\sigma$ and $2\sigma$ CLs, respectively. Thus, we conclude that the DD relation is compatible with present observations.