### Abstract

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 the 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 (BAF) and type Ia supernovae (SNeIa) 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 Δτ in the optical depth from redshift 0.20 to 0.35 at visible wavelengths to Δτ < 0.13 at 95% confidence. In a model with a constant comoving number density n of scatterers of constant proper cross section σ, this limit implies nσ < 2 × 10 ^{-4} h Mpc^{-1}. These limits depend weakly on the cosmological world model. Assuming a concordance world model, the best-fit value of Δτ to current data is negative at the 2σ level. This could signal interesting new physics or could be the result of unidentified systematics in the BAF/SNeIa measurements. Within the next few years, the limits on transparency could extend to redshifts z 2.5 and improve to nσ < 1.1 × 10^{-5} h Mpc^{-1}. Cosmic variance will eventually limit the sensitivity of any test using the BAF at the nσ ∼ 4 × 10^{-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.

Original language | English (US) |
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Pages (from-to) | 1727-1732 |

Number of pages | 6 |

Journal | Astrophysical Journal |

Volume | 696 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 10 2009 |

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### Keywords

- cosmological parameters
- cosmology: observations
- large-scale structure of universe
- radiative transfer
- relativity
- supernovae: general

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal*,

*696*(2), 1727-1732. https://doi.org/10.1088/0004-637X/696/2/1727