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

TL;DR

This paper shows that Type Ia supernovae observations critically limit the ability of late-time expansion modifications to fully resolve the Hubble tension, with current data constraining the maximum achievable H0 to about 69.

Contribution

It demonstrates that SNe Ia data impose fundamental constraints on late-time expansion models aimed at resolving the Hubble tension, highlighting a key obstacle.

Findings

Late-time $w(z)$ deformations can reconcile some data tensions.

No viable solutions with $H_0 > 69$ satisfy SNe Ia constraints.

Maximum achievable $H_0$ is about 69.09 with current data.

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 $H_0 = 69.09\pm0.30$ ($\chi^2_{\rm BF} \approx \chi^2_{\Lambda\rm CDM}$) 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.