Cosmic transparency: A test with the baryon acoustic feature and type Ia   supernovae
  Conservation of the phase-space density of photons plus Lorentz invariance requires that the cosmological luminosity distance be larger than the angular diameter distance by a factor of $(1+z)^2$, where $z$ is the redshift. Because this is a fundamental symmetry, this prediction--known sometimes as the "Etherington relation" or the "Tolman test"--is independent of world model, or even the assumptions of homogeneity and isotropy. It depends, however, on Lorentz invariance and transparency. Transparency can be affected by intergalactic dust or interactions between photons and the dark sector. Baryon acoustic feature and type Ia supernovae measures of the expansion history are differently sensitive to the angular diameter and luminosity distances and can therefore be used in conjunction to limit cosmic transparency. At the present day, the comparison only limits the change $\Delta\tau$ in the optical depth from redshift 0.20 to 0.35 at visible wavelengths to $\Delta\tau < 0.13$ at 95% confidence. In a model with a constant comoving number density $n$ of scatterers of constant proper cross-section $\sigma$, this limit implies $n \sigma< 2\times10^{-4} h \Mpc^{-1}$. These limits depend weakly on the cosmological world model. Within the next few years, the limits could extend to redshifts $z\approx2.5$ and improve to $n \sigma<1.1 \times10^{-5} h \Mpc^{-1}$. Cosmic variance will eventually limit the sensitivity of any test using the BAF at the $n \sigma\sim 4\times10^{-7} h \Mpc^{-1}$ level. Comparison with other measures of the transparency is provided; no other measure in the visible is as free of astrophysical assumptions. 
Surhud More, Jo Bovy, David W. Hogg