Etherington Duality Violation Hints

Etherington’s distance–duality relation, D_L = (1+z)² D_A, must hold in any metric theory of gravity with photon number conservation and light following null geodesics, yet combined analyses of supernova luminosity distances, cluster and BAO angular-diameter distances, and strong-lensing systems show mild but persistent hints of percent-level deviations from this relation (Etherington 1933; Renzi 2022). These apparent violations force ΛCDM either to invoke subtle, redshift-dependent systematics in SNe, clusters, lensing, or opacity, or else to contemplate new physics affecting photon propagation or geometry, which in turn complicates attempts to resolve the H0 and dark-energy tensions in a self-consistent way (Uzan et al. 2004; Teixeira et al. 2025).

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