Statistical Test of Distance–Duality Relation with Type Ia Supernovae and Baryon Acoustic Oscillations

Abstract

We test the distance–duality relation between cosmological luminosity distance ( ) from the JLA SNe Ia compilation and angular-diameter distance ( ) based on Baryon Oscillation Spectroscopic Survey (BOSS) and WiggleZ baryon acoustic oscillation measurements. The measurements are matched to redshift by a statistically consistent compression procedure. With Monte Carlo methods, nontrivial and correlated distributions of η can be explored in a straightforward manner without resorting to a particular evolution template . Assuming independent constraints on cosmological parameters that are necessary to obtain and values, we find 9% constraints consistent with η  = 1 from the analysis of SNIa + BOSS and an 18% bound results from SNIa + WiggleZ. These results are contrary to previous claims that η  < 1 has been found close to or above the 1 σ level. We discuss the effect of different cosmological parameter inputs and the use of the apparent deviation from distance–duality as a proxy of systematic effects on cosmic distance measurements. The results suggest possible systematic overestimation of SNIa luminosity distances compared with data when a Planck ΛCDM cosmological parameter inference is used to enhance the precision. If interpreted as an extinction correction due to a gray dust component, the effect is broadly consistent with independent observational constraints.