Statistical Test of Distance--Duality Relation with Type Ia Supernovae
  and Baryon Acoustic Oscillations
  We test the distance--duality relation $\eta \equiv d_L / [ (1 + z)^2 d_A ] =
1$ between cosmological luminosity distance ($d_L$) from the JLA SNe Ia
compilation (arXiv:1401.4064) and angular-diameter distance ($d_A$) based on
Baryon Oscillation Spectroscopic Survey (BOSS; arXiv:1607.03155) and WiggleZ
baryon acoustic oscillation measurements (arXiv:1105.2862, arXiv:1204.3674).
The $d_L$ measurements are matched to $d_A$ redshift by a statistically
consistent compression procedure. With Monte Carlo methods, nontrivial and
correlated distributions of $\eta$ can be explored in a straightforward manner
without resorting to a particular evolution template $\eta(z)$. Assuming
independent constraints on cosmological parameters that are necessary to obtain
$d_L$ and $d_A$ values, we find 9% constraints consistent with $\eta = 1$ from
the analysis of SNIa + BOSS and an 18% bound results from SNIa + WiggleZ. These
results are contrary to previous claims that $\eta < 1$ has been found close to
or above the $1 \sigma$ 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 $d_A$ data when a Planck {\Lambda}CDM cosmological parameter
inference (arXiv:1502.01589) 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.
