New constraints on the distance duality relation from the local data

TL;DR

This study tests the cosmic distance duality relation using local data from supernovae, galaxy clusters, and BAO, finding no evidence of violation and constraining possible deviations.

Contribution

It introduces a method to test DDR violation using local data with two parameterizations, providing new constraints on potential deviations.

Findings

Elliptical clusters + BAO data tightly constrain η₀ near zero.

Spherical clusters + BAO data have large uncertainties, limiting constraints.

No significant evidence for DDR violation was found.

Abstract

The cosmic distance duality relation (DDR), which connects the angular diameter distance and luminosity distance through a simple formula $D_A(z)(1+z)^2/D_L(z)\equiv1$, is an important relation in cosmology. Therefore, testing the validity of DDR is of great importance. In this paper, we test the possible violation of DDR using the available local data including type Ia supernovae (SNe Ia), galaxy clusters and baryon acoustic oscillations (BAO). We write the modified DDR as $D_A(z)(1+z)^2/D_L(z)=\eta(z)$, and consider two different parameterizations of $\eta(z)$, namely $\eta_1(z)=1+\eta_0 z$ and $\eta_2(z)=1+\eta_0 z/(1+z)$. The luminosity distance from SNe Ia are compared with the angular diameter distance from galaxy clusters and BAO at the same redshift. Two different cluster data are used here, i.e. elliptical clusters and spherical clusters. The parameter $\eta_0$ is obtained using the Markov chain Monte Carlo methods. It is found that $\eta_0$ can be strictly constrained by the elliptical clusters + BAO data, with the best-fitting values $\eta_0=-0.04\pm 0.12$ and $\eta_0=-0.05\pm 0.22$ for the first and second parametrizations, respectively. However, the spherical clusters + BAO data couldn't strictly constrain $\eta_0$ due to the large intrinsic scatter. In any case studied here, no evidence for the violation of DDR is found.