Effective distance-duality deformations as a diagnostic oflate-time calibration tensions

Abstract The Hubble tension between the SH0ES-calibrated luminosity-distance scale and the CMB/BAO-inferred expansion history can be recast as an effective violation of the distance-duality relation (DDR), $\eta(z)\equiv D_L(z)/[(1+z)^2D_A(z)]$. Using the Fisher-bias formalism, we explore how an overall distance recalibration and a broad redshift variation can accommodate different cosmological responses. These diagnostic profiles guide a compact model of the distance deformation. We adopt a three-parameter tanh parameterization and perform full MCMC sampling with Planck, DESI-DR2 BAO, Pantheon+ with SH0ES, and cosmic chronometers. The tanh and constant-DDR models give $\Delta\chi^2_{\rm tanh/\Lambda CDM}=-35.1$ and $\Delta\chi^2_{\rm const/\Lambda CDM}=-31.5$, respectively; the additional redshift-dependent contribution is therefore $\Delta\chi^2_{\rm tanh/const}=-3.6$. Redshift dependence is marginally preferred ($\sim1.4\sigma$), while neither the Bayesian evidence nor the deviance information criterion provides meaningful support for the extension. We thus find no significant evidence for redshift-dependent DDR violation, while the dominant constant offset remains degenerate with a recalibration of the supernova absolute magnitude $M_B$ in the absence of an external calibration. The combined analysis returns $H_0=68.44\pm0.30$\,km\,s$^{-1}$\,Mpc$^{-1}$ and $\Omega_m=0.301\pm0.004$. Finally, at the background level, the adopted SN-sector deformation is strongly degenerate with the specific evolving-dark-energy model considered here.