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

Zhihuan Zhou, Zhuang Miao, Sheng Bi, Chaoqian Ai, Hongchao Zhang

TL;DR

This work tests whether minimal late-time expansions, implemented as perturbations $\Delta w(z)$ to the dark-energy EoS, can resolve the $H_0$ tension without sacrificing fit quality. Using a Fisher-bias framework, the authors optimize $\Delta w(z)$ to shift the Hubble parameter $H(z)$ while keeping $\Delta \chi^2$ nonpositive and maintaining consistency with data from cosmic chronometers, DESI DR2 BAO, Pantheon+ SNe Ia, and Planck distance priors. They find that BAO-driven perturbations can reconcile DESI BAO with SH0ES and modestly raise Planck-derived $H_0$, but including Pantheon+ SNe Ia imposes strong constraints that prevent a universal solution with $H_0$ above about 69 km s$^{-1}$ Mpc$^{-1}$; MCMC validation confirms the best achievable $H_0$ is around $69.1\pm0.3$ with acceptable fit, yet the required late-time $w(z)$ features conflict with SNe Ia. Consequently, late-time modifications alone cannot fully resolve the Hubble tension in a self-consistent way, suggesting the need for combined early- and late-Universe physics or more radical cosmological frameworks.

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 ($Δχ^2 < 0$ relative to $Λ$CDM); (ii) In the neighborhood of Planck best-fit $Λ$CDM model, no cosmologically viable solutions targeting $H_0 \gtrsim 69$ satisfy SNe Ia constraints. MCMC validation confirms the maximum achievable $H_0 = 69.09\pm0.30$ ($χ^2_{\rm BF} \approx χ^2_{Λ\rm CDM}$) 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.

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

TL;DR

This work tests whether minimal late-time expansions, implemented as perturbations to the dark-energy EoS, can resolve the tension without sacrificing fit quality. Using a Fisher-bias framework, the authors optimize to shift the Hubble parameter while keeping nonpositive and maintaining consistency with data from cosmic chronometers, DESI DR2 BAO, Pantheon+ SNe Ia, and Planck distance priors. They find that BAO-driven perturbations can reconcile DESI BAO with SH0ES and modestly raise Planck-derived , but including Pantheon+ SNe Ia imposes strong constraints that prevent a universal solution with above about 69 km s Mpc; MCMC validation confirms the best achievable is around with acceptable fit, yet the required late-time features conflict with SNe Ia. Consequently, late-time modifications alone cannot fully resolve the Hubble tension in a self-consistent way, suggesting the need for combined early- and late-Universe physics or more radical cosmological frameworks.

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 (via reconstruction) can reconcile tensions between CC, Planck, DESI BAO, and SH0ES measurements while maintaining or improving fit quality ( relative to CDM); (ii) In the neighborhood of Planck best-fit CDM model, no cosmologically viable solutions targeting satisfy SNe Ia constraints. MCMC validation confirms the maximum achievable () across all data combinations, indicating that the conflict between late-time modifications and SNe Ia observations prevents complete resolution of the Hubble tension.

Paper Structure

This paper contains 16 sections, 12 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Fisher-Bias Formalism and Hubble Optimization
  4. Functional Expansion and Response Theory
  5. Hubble Perturbation Minimization
  6. STATISTICAL METHODOLOGY AND DATASETS
  7. DESI BAO (DR2)
  8. Pantheon+ Supernovae
  9. Cosmic Chronometers
  10. Planck datasets
  11. RESULTS AND DISCUSSIONS
  12. Resolution of CMB-BAO-SH0ES Tension
  13. Conflicts with Pantheon+ SNe Ia
  14. MCMC Validation of Fisher-Bias Solutions
  15. $S_8$($\Omega_{m,0}$) Tensions
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Solutions for $w(z\lesssim 2)$ given target value of $H_0$. The vertical panels show solutions for: (a) cosmic chronometers (CC) data with maximum target $H_0 = 73.17$; (b) DESI BAO measurements ($H_0 = 73.17$); (c) Pantheon+ SNe combined with Planck distance prior ($H_0 = 69.0$); and (d) the full combination of BAO+CC+SNe data with target $H_0 = 69.0$). All solutions preserve the Planck $\Lambda$CDM best-fit parameters.
  • Figure 2: Upper panel: The DE EoS $w(z)$ showing solutions from cosmic chronometers (CC) alone (blue), DESI BAO (orange), BAO+Planck distance prior (PLC)+SNe (green), and the full combination CC+BAO+SNe (red). Lower panel: Corresponding evolution of the relative DE density $\rho_{\rm fld}(z)/\rho_{\rm crit,0}$ for each case. All solutions with targeting best-fit parameters ($H_0 = 70.0$, $\omega_b = 0.02237$, $\omega_{\rm cdm} = 0.1200$) while optimizing the late-time expansion history through Fisher-bias analysis.
  • Figure 3: Constraints on cosmological parameters for the three compared models (F1, F2, $\Lambda$CDM) from different data combinations. The upper panel displays constraints from DESI BAO and cosmic chronometers (CC) data, while the lower panel incorporates additional Planck distance prior (PLC) measurements. All contours show $1\sigma$ and $2\sigma$ confidence regions. The Fisher-bias optimized models target different Hubble constant values: F1-BAO for $H_0 = 73.0$ and F2-SN for $H_0 = 69.0$.
  • Figure 4: Cosmological parameter constraints for the Fisher-bias optimized models from different data combinations. The upper panel shows the F1 model targeting $H_0 = 73.0$, while the lower panel displays the F2 model targeting $H_0 =$. For each model, we show three data combinations: (i) DESI BAO + CC, (ii) BAO + CC + Planck , and (iii) BAO + CC + Planck + SNe. All contours represent $1\sigma$ and $2\sigma$ confidence regions.