Cosmic acceleration vs axion-photon mixing

Axion-photon mixing has been proposed as an alternative to acceleration as the explanation for supernovae dimming. We point out that the loss of photons due to this mixing will induce a strong asymmetry between the luminosity, d_L(z), and angular-diameter distance, d_A(z), since the latter is unaffected by mixing. In a first search for such an asymmetry we introduce a dimensionless mixing amplitude lambda so that lambda=0 if no photons are lost and lambda = 1 if axion-photon mixing occurs. The best-fit to SNIa and radio galaxy data is lambda = -0.3^{+0.6}_{-0.4} (95% CL), corresponding to an unphysical, negative, mixing length. This same argument limits the attenuation of light from supernovae due to dust. We show that future d_L and d_A data from SNAP and galaxy surveys such as DEEP2 and KAOS will detect or rule out mixing at more than 5-sigma, almost independently of the dark energy dynamics. Finally we discuss the constraints from the near maximal polarisation of the gamma-ray burst (GRB) GRB021206. Since mixing reduces the polarisation of distant sources, future observations of high redshift GRBs may provide orthogonal constraints on axion-photon mixing and related scenarios.