Implications for dark energy of cosmic transparency in light of DESI data

ABSTRACT The distance duality relation (DDR) between luminosity and angular diameter distances holds if gravity is described by a metric theory and the Universe is transparent. Recent cosmological inferences have suggested that dark energy may evolve in time. We test how DDR impacts dark energy inference. We find no deviation from the DDR, independent of the SN Ia compilation used, or the assumed dark energy model. This corresponds to a maximum deviation in the SN Ia luminosity of $\Delta m \sim 0.05$ mag at the highest redshift. Allowing for deviations in the DDR increases the errors in the dark energy equation of state parameters by 30–50 per cent. For the Pantheon+ compilation the constraints on dark energy are within $2\sigma$ of $\Lambda$CDM when applying a more realistic minimum redshift cut $z_{\rm min} \gt 0.023$. We constrain photon–axion mixing and the presence of (grey) intergalactic (IG) dust to $\Omega _{\rm dust}\lt 2 \times 10^{-4}$ at 95 per cent C.L. and on photon–axion interaction length scale $g_{a\gamma } \lt 10^{-12}\, {\rm GeV}^{-1}$. With the local Cepheid calibration of the SNe Ia absolute luminosity, a significant deviation from the DDR relation (for which $\epsilon =0$) is preferred. The best-fitting parameter value $\epsilon = -0.091 \pm 0.024$ requires the SNe Ia to be brighter than the case with DDR valid, hence, neither of the physical scenarios which dim the SNe can explain the high $H_0$. We expect improvements by a factor of ${\sim} 2$ with future data.