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

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 using Type Ia supernovae (SNe~Ia), baryon acoustic oscillation (BAO) and the cosmic microwave background (CMB) observations have suggested that dark energy may evolve in time. We test how the assumption of distance duality impacts dark energy inference. Marginalizing over the absolute SNe~Ia luminosity, we find no deviation from the DDR, independent of the SN~Ia compilation used, or the assumed dark energy model. This corresponds 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 (EoS) by 30-50$\%$. For the Pantheon+ compilation the constraints on dark energy are within $2\sigma$ of $\Lambda$CDM when applying a more realistic minimum redshift cut $z_{\rm min} >0.023$. We constrain possible physical scenarios that can impact cosmic transparency, specifically photon-axion mixing and the presence of (gray) intergalactic (IG) dust, in the latter case limiting the dust density to $\Omega_{\rm dust}<2 \times 10^{-4}$ at 95\% C.L. When using the local Cepheid calibration of the SNe~Ia absolute luminosity, a significant deviation from the DDR relation (for which $\epsilon=0$) is preferred. However, the best fit parameter value $\epsilon = -0.091 \pm 0.024$ requires the SNe~Ia to be brighter than the case with DDR valid, therefore, neither of the physical scenarios which dim the SNe can explain the high $H_0$. Constraints on the photon-axion interaction length scale suggest a limit on the coupling constant of $g_{a\gamma} < 10^{-12}\,{\rm GeV}^{-1}$.