Implications of distance duality violation for the $H_0$ tension and evolving dark energy

Understand

We investigate whether a violation of the distance duality relation (DDR), $D_L(z) = (1+z)^2 D_A(z)$, connecting the angular diameter and luminosity distances, can explain the Hubble tension and alter the evidence for dynamical dark energy in recent cosmological observations.

• We constrain five phenomenological parameterisations of DDR violation using Baryon Acoustic Oscillation measurements from the DESI survey calibrated with the sound horizon derived from \textit{Planck} Cosmic Microwave Background data and the Pantheon+ Type Ia supernova (SNIa) catalogue calibrated with the supernova absolute magnitude from S$H_0$ES.
• We find that two toy models can resolve the tension: a constant offset in the DDR (equivalent to a shift in the calibration of the SNIa data), $D_L(z)/D_A(z)\simeq 0.925(1+z)^2$, which leaves the hint for evolving dark energy unaffected; or a change in the power-law redshift-dependence of the DDR, restricted to $z\lesssim 1$, $D_L(z)/D_A(z)\simeq(1+z)^{1.866}$, together with a {\it constant} phantom dark energy equation of state $w\sim -1.155$.
• The Bayesian evidence slightly favours the latter model.