Redshift-dependent Distance Duality Violation in Resolving Multidimensional Cosmic Tensions

Abstract: In this work, we investigate whether violations of the distance-duality relation (DDR) can resolve the multidimensional cosmic tensions characterized by the $H_0$ and $S_8$ discrepancies. Using the Fisher-bias formalism, we reconstruct minimal, data-driven $\eta(z)$ profiles that capture the late-time deviations required to reconcile early- and late-Universe calibrations. While a constant DDR offset preserves the Pantheon-inferred matter density $\Omega_m = 0.334 \pm 0.018$--leaving its inconsistency with the Planck best-fit $\Lambda$CDM model and weak-lensing surveys unresolved--a time-varying DDR substantially reduces cross-dataset inconsistencies and improves the global fit, yielding $\Delta\chi^2 \simeq -10$ relative to $\Lambda$CDM when the SH0ES prior is excluded. This result suggests that the $\Omega_m$ discrepancy may represent indirect evidence for a time-varying DDR. A hybrid scenario combining a time-dependent DDR with a phantom-like dark energy transition achieves the most consistent global reconciliation, reducing the tension with DES-Y3 measurements to below $2\sigma$. These findings indicate that a mild DDR violation, coupled with evolving dark energy, offers a coherent pathway toward jointly addressing the $H_0$ and $S_8$ tensions.