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Redshift-dependent Distance Duality Violation in Resolving Multidimensional Cosmic Tensions

Zhihuan Zhou, Zhuang Miao, Rong Zhang, Hanbing Yang, Penghao Fu, Chaoqian Ai

TL;DR

This work addresses the multidimensional cosmological tensions by exploring redshift-dependent violations of the distance-duality relation through the DDR proxy $\eta(z)$. Using a Fisher-bias formalism, the authors reconstruct minimal, data-driven DDR deformations—employing Gaussian and top-hat basis functions—to reconcile Pantheon+SH0ES with CMB+BAO constraints, and validate these reconstructions with full MCMC analyses. They compare three models: a constant DDR offset (M1-Const), a time-dependent DDR (M2-TimeDep), and a hybrid DDR plus phantom-like dark energy (M3-Hybrid); while a constant offset modestly reduces $H_0$ tension, a time-dependent DDR significantly improves global fits, and the hybrid model yields the strongest, most consistent reconciliation across all datasets, lowering the DES-Y3 tension to below $2\sigma$ and stabilizing $\Omega_{m,0}\approx0.28$ with $S_8\approx0.796$. A key finding is a degeneracy between DDR violation and evolving dark energy, indicating that breaking this degeneracy requires independent measurements of the expansion history, such as cosmic chronometers or radial BAO, to disentangle geometry from dynamics. Overall, the results motivate a physically motivated, mild DDR violation in concert with evolving dark energy as a viable pathway to jointly addressing the $H_0$ and $S_8$ tensions, while highlighting the need for concrete mechanisms behind DDR deviations.

Abstract

In this work, we investigate whether violations of the distance-duality relation (DDR) can resolve the multidimensional cosmic tensions characterized by the $H_0$ and $S_8$ discrepancies. Using the Fisher-bias formalism, we reconstruct minimal, data-driven $η(z)$ profiles that capture the late-time deviations required to reconcile early- and late-Universe calibrations. While a constant DDR offset preserves the Pantheon-inferred matter density $Ω_m = 0.334 \pm 0.018$--leaving its inconsistency with the Planck best-fit $Λ$CDM model and weak-lensing surveys unresolved--a time-varying DDR substantially reduces cross-dataset inconsistencies and improves the global fit, yielding $Δχ^2 \simeq -10$ relative to $Λ$CDM when the SH0ES prior is excluded. This result suggests that the $Ω_m$ discrepancy may represent indirect evidence for a time-varying DDR. A hybrid scenario combining a time-dependent DDR with a phantom-like dark energy transition achieves the most consistent global reconciliation, reducing the tension with DES-Y3 measurements to below $2σ$. These findings indicate that a mild DDR violation, coupled with evolving dark energy, offers a coherent pathway toward jointly addressing the $H_0$ and $S_8$ tensions.

Redshift-dependent Distance Duality Violation in Resolving Multidimensional Cosmic Tensions

TL;DR

This work addresses the multidimensional cosmological tensions by exploring redshift-dependent violations of the distance-duality relation through the DDR proxy . Using a Fisher-bias formalism, the authors reconstruct minimal, data-driven DDR deformations—employing Gaussian and top-hat basis functions—to reconcile Pantheon+SH0ES with CMB+BAO constraints, and validate these reconstructions with full MCMC analyses. They compare three models: a constant DDR offset (M1-Const), a time-dependent DDR (M2-TimeDep), and a hybrid DDR plus phantom-like dark energy (M3-Hybrid); while a constant offset modestly reduces tension, a time-dependent DDR significantly improves global fits, and the hybrid model yields the strongest, most consistent reconciliation across all datasets, lowering the DES-Y3 tension to below and stabilizing with . A key finding is a degeneracy between DDR violation and evolving dark energy, indicating that breaking this degeneracy requires independent measurements of the expansion history, such as cosmic chronometers or radial BAO, to disentangle geometry from dynamics. Overall, the results motivate a physically motivated, mild DDR violation in concert with evolving dark energy as a viable pathway to jointly addressing the and tensions, while highlighting the need for concrete mechanisms behind DDR deviations.

Abstract

In this work, we investigate whether violations of the distance-duality relation (DDR) can resolve the multidimensional cosmic tensions characterized by the and discrepancies. Using the Fisher-bias formalism, we reconstruct minimal, data-driven profiles that capture the late-time deviations required to reconcile early- and late-Universe calibrations. While a constant DDR offset preserves the Pantheon-inferred matter density --leaving its inconsistency with the Planck best-fit CDM model and weak-lensing surveys unresolved--a time-varying DDR substantially reduces cross-dataset inconsistencies and improves the global fit, yielding relative to CDM when the SH0ES prior is excluded. This result suggests that the discrepancy may represent indirect evidence for a time-varying DDR. A hybrid scenario combining a time-dependent DDR with a phantom-like dark energy transition achieves the most consistent global reconciliation, reducing the tension with DES-Y3 measurements to below . These findings indicate that a mild DDR violation, coupled with evolving dark energy, offers a coherent pathway toward jointly addressing the and tensions.

Paper Structure

This paper contains 15 sections, 13 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Reconstruction of Late-Time Distance Duality
  4. Reconstructed $\eta(z)$ Profiles
  5. Joint $\eta(z)$--$H(z)$ Deformation and the $\omega_c$--$H_0$ Coupling
  6. Statistical Methodology and Datasets
  7. DESI BAO (DR2)
  8. Pantheon+SH0ES Supernovae
  9. Cosmic Chronometers
  10. Planck datasets
  11. MCMC Analysis
  12. Model Contrast
  13. Degeneracy between DDR Violation and Evolving Dark Energy
  14. Resolution of the Multi-dimensional Tensions
  15. Conclusion

Figures (6)

  • Figure 1: Solutions for $\eta(z)$ profiles given target values of $H_0$ and $\Omega_m$. The vertical panels show solutions for: (a) fixed $\Omega_m = 0.338$ with different target $H_0$ values; (b) fixed $H_0 = 69.0$ with different target $\Omega_m$ values. The right panels display the reconstructed $\eta(z)$ profiles, while the left panels show the normalized deviation defined as $(\eta(z) - \bar{\eta})/|\bar{\eta}|$.
  • Figure 2: Reconstructed $w(z)$ and $\eta(z)$ profiles based on BAO data. The upper panels show the $w(z)$ profile reconstructed using BAO and $r_s$ derived from the CMB likelihood, with $\omega_c = 0.1202$ and a fixed target $H_0$. The lower panels display the corresponding $\eta(z)$ profiles obtained using the Fisher-bias method, with the same $\omega_c$ and $H_0$ target. All solutions preserve the Planck $\Lambda$CDM best-fit parameters.
  • Figure 3: Comparison of $\eta(z)$ profiles reconstructed using Gaussian and Top-hat basis functions. The solid line represents the result obtained using Gaussian basis functions (M2-Timdep model), while the dashed line corresponds to the Top-hat basis result. Both profiles are derived from the Pantheon+SH0ES likelihood, with target parameters fixed to the best-fit values from the Planck + BAO $\Lambda$CDM model ($\omega_c = 0.1202$, $H_0 = 0.684$).
  • Figure 4: Constraints on cosmological parameters for the three compared models (M1-Const, M2-TimeDep, M2-Hybrid) from different data combinations. The "M$-$" label denotes data combinations excluding the SH0ES prior, specifically including CC + BAO + SNe + Planck likelihoods, while "M$+$" indicates the same combinations with the SH0ES calibration incorporated.
  • Figure 5: Cosmological parameter constraints from different data combinations. The upper panel shows the M1-Const model targeting ($\eta = 0.925$), while the lower panel displays the M2-TimeDep model. For each model, we show two data combinations: (i) BAO + CC + Planck + SNe , and (ii) BAO + CC + Planck + SNe + SH0ES. All contours represent $1\sigma$ and $2\sigma$ confidence regions.
  • ...and 1 more figures