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 (CCs), baryon acoustic oscillations (BAOs) from Dark Energy Spectroscopic Instrument (DESI) Data Release 2, Planck cosmic microwave background, and $\mathrm{Pantheon}+\text{data}$, 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 [$\mathrm{\Delta }{\chi }^2<0$ relative to $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$)]. (ii) In the neighborhood of the Planck best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model, no cosmologically viable solutions targeting $H_0\gtrsim 69$ satisfy SNe Ia constraints. Markov chain Monte Carlo validation confirms the maximum achievable $H_0=69.15\pm 0.32$ (${\chi }_{\mathrm{BF}}^2\approx {\chi }_{\mathrm{\Lambda }\mathrm{CDM}}^2$) 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.

Close

PrevNext

View figure in article

• Cosmological parameters
• Dark energy
• Evolution of the Universe