What Prevents Resolving the Hubble Tension through Late-Time Expansion Modifications?

Abstract

We demonstrate that Type Ia supernovae (SNe Ia) observations impose the critical constraint for resolving the Hubble tension through late-time expansion modifications. Applying the Fisher-bias optimization framework to cosmic chronometers (CC), baryon acoustic oscillations (BAO) from DESI DR2, Planck CMB, and Pantheon+ data, we find that: (i) deformations in $H(z\lesssim 3)$ (via $w(z)$ reconstruction) can reconcile tensions between CC, Planck, DESI BAO, and SH0ES measurements while maintaining or improving fit quality ($\Delta {\chi }^2<0$ relative to $\Lambda$CDM); (ii) In the neighborhood of Planck best-fit $\Lambda$CDM model, no cosmologically viable solutions targeting $H_0\gtrsim 69$ satisfy SNe Ia constraints. MCMC validation confirms the maximum achievable $H_0=69.09\pm 0.30$ (${\chi }_{\mathrm{BF}}^2\approx {\chi }_{\Lambda \mathrm{CDM}}^2$) across all data combinations, indicating that the conflict between late-time $w(z)$ modifications and SNe Ia observations prevents complete resolution of the Hubble tension.

10 pages, 4 figures

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