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The Etherington distance duality relation, which relates the luminositydistance, the angular diameter distance and the redshift of objects, dependsonly upon a conservation law for light that traces back directly to theLorentzian spacetime geometry. We show that this duality relation indeedsurvives transition to the most general linear electrodynamics withoutbirefringence, which rests on a spacetime geometry constituted by a Lorentzianmetric and two scalar fields, a dilaton and an axion. By computing the Poyntingvector and optical scalar transport in the geometrical optics limit of thisframework, we derive the modification of the light flux in the presence of adilaton field and present improved constraints on the gradient of the dilatonfield from observations of the Cosmic Microwave Background spectrum. Althoughthis flux modification may seem applicable also to fundamental modifications ofthe Etherington relation, we show that the distance duality relation stillholds true. Thus any deviations within this classical theory would implynon-metricities, once astrophysical sources for attenuation, such as dust, areaccounted for. Moreover, using the most up-to-date measurements of theluminosity distances to Supernovae of Type Ia, and the inferred angulardiameter distances from the baryon acoustic feature measurements, we perform ascale-free and nearly model-independent test of the Etherington distanceduality relation between redshifts of $0.38$ and $0.61$. We find consistencywith the standard distance duality relation and constrain the optical depth oflight between these two redshifts to $\Delta\tau=-0.006\pm0.046$.

Modifications to the Etherington Distance Duality Relation and Observational Limits