Any unified early and late dark energy scenario with a single tracking scalar field requires a potential with three distinct slopes arranged in a steep-steeper-shallow hierarchy.
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On the implications of the `cosmic calibration tension' beyond $H_0$ and the synergy between early- and late-time new physics
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abstract
The `cosmic calibration tension' is a $> 5\sigma$ discrepancy between the cosmological distance ladder built from baryonic acoustic oscillations (BAO) calibrated by the Planck/$\Lambda$CDM sound horizon ($r_s$) and Type Ia supernovae (SN1a) calibrated instead with the S$H_0$ES absolute magnitude, assuming the distance-duality relationship (DDR) holds. In this work, we emphasize the consequences of this tension beyond the value of the Hubble constant $H_0$, and the implications for physics beyond $\Lambda$CDM. Of utmost importance, it implies a larger physical matter density $\omega_m\equiv \Omega_m h^2$, as both the fractional matter density $\Omega_m$ and $h\equiv H_0/100$ km/s/Mpc are well constrained from late-time data. New physics in the pre-recombination era must thus be able to decrease $r_s$ while either reducing the value of $\Omega_m$, or increasing the value of $\omega_m$. Assuming a $\Lambda$CDM-like primordial power spectrum, this necessarily results in an increase in the clustering amplitude $\sigma_8$. Deviations from $\Lambda$CDM in the late-time expansion history cannot resolve the calibrator tension but can help relax the required shifts to the matter density and $\sigma_8$: it is in that sense that a combination of early and late-time new physics may help alleviate the tension. More precisely, models that modify the pre-recombination expansion history can accommodate the increase in $\omega_m$ without the need for additional modifications. It is those models which only affect recombination that require additional deviations at late-times to be successful. Hence, the `cosmic calibration tension' points either to a targeted modification of the pre-recombination expansion history, or to a broader change affecting multiple cosmic epochs.
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astro-ph.CO 18representative citing papers
For fixed sound-horizon and supernova calibrations, no late-time modification—even one violating cosmic distance duality—can resolve the Hubble tension, because the required ~8-10% CDDR violation is excluded by BAO, cosmic-chronometer, and CMB spectral constraints.
A geometric invariance makes the BAO-SN Ω_m gap invariant under sound-horizon rescaling α and requires opposite w(z) deformations for the two datasets, so their combination cannot reach the local H0 value.
Model-independent reconstruction shows that early-universe modifications resolving the Hubble tension exist at the background level, requiring a smooth ~15% pre-recombination expansion rate enhancement.
Two-field axion-like early dark energy reduces Hubble tension to 1.5 sigma residual and improves high-ell CMB fits over single-field models.
Bootstrap symbolic regression of SN+BAO data yields mild 2–4σ FLRW consistency deviations and a density field still compatible with both Planck and SH0ES ΛCDM.
Two model-independent methods applied to latest SN and BAO data find the cosmic distance duality relation consistent with observations within 1 sigma and no evidence of violation.
Under standard recombination, phantom-crossing dynamical dark energy is preferred at ~97–98.5% probability; early-time fixes to the Hubble tension erase that preference while creating severe ω_m tension with CMB.
EDE models increase inferred α_s from CMB data, strengthening tension with USR PBH models that predict negative running.
Using Planck, DESI, supernovae, and redshift-space distortions, the authors infer that modified gravity, if present, must act only below ~30 Mpc and cannot modify the large scales previously considered.
A phenomenological redshift-dependent SNIa magnitude correction shows no evidence in ΛCDM but is preferred at 4.3σ with dynamical dark energy, reducing Hubble tension to 1.5σ.
Exponential IR f(T) gravity Model I alleviates Hubble tension but is disfavoured by combined Planck/ACT/SPT+DESI+Pantheon+ data; Model II is ruled out because background constraints force unphysical shifts in CMB parameters.
Perturbative modifications to the electron mass m_e(z) resolve the Hubble tension with Planck+ACT CMB data but cannot when DESI DR2 BAO data are added due to lowered Omega_m.
Local Hubble constant anisotropy in Cosmicflows-4 data is primarily attributed to peculiar velocities and survey structure rather than cosmic-scale isotropy violation, with limited implications for the Hubble tension.
Extended analysis of DESI DR2 data confirms robust evidence for dynamical dark energy with phantom crossing preference, stable under parametric and non-parametric modeling.
Pure early or late fixes to the Hubble tension are tightly constrained; remaining options are combined early-late interacting dark energy or new physics at the local-to-homogeneous transition.
An extended model with decaying dark matter around equality and w0 dark energy yields H0 ≈ 70 km/s/Mpc from Planck+ACT+DESI data, reducing Hubble tension to ~2.2σ while producing Bayesian evidence comparable to ΛCDM.
No significant violation of the cosmic distance duality relation is detected across multiple parameterizations, with flat cosmologies preferred by model selection.
citing papers explorer
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Unifying Early and Late Dark Energy: Dynamical Requirements and Obstructions
Any unified early and late dark energy scenario with a single tracking scalar field requires a potential with three distinct slopes arranged in a steep-steeper-shallow hierarchy.
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Can Distance Duality Violation Save Late-time Solutions to the Hubble Tension?
For fixed sound-horizon and supernova calibrations, no late-time modification—even one violating cosmic distance duality—can resolve the Hubble tension, because the required ~8-10% CDDR violation is excluded by BAO, cosmic-chronometer, and CMB spectral constraints.
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Geometric obstruction to resolving the Hubble tension: orthogonality of scale and shape in distance measurements
A geometric invariance makes the BAO-SN Ω_m gap invariant under sound-horizon rescaling α and requires opposite w(z) deformations for the two datasets, so their combination cannot reach the local H0 value.
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Geometric Constraints on the Pre-Recombination Expansion History from the Hubble Tension
Model-independent reconstruction shows that early-universe modifications resolving the Hubble tension exist at the background level, requiring a smooth ~15% pre-recombination expansion rate enhancement.
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Double the axions, half the tension: multi-field early dark energy eases the Hubble tension
Two-field axion-like early dark energy reduces Hubble tension to 1.5 sigma residual and improves high-ell CMB fits over single-field models.
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Model-independent constraints on generalized FLRW consistency relations with bootstrap-based symbolic regression
Bootstrap symbolic regression of SN+BAO data yields mild 2–4σ FLRW consistency deviations and a density field still compatible with both Planck and SH0ES ΛCDM.
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Model-independent test of the cosmic distance duality relation with recent observational data
Two model-independent methods applied to latest SN and BAO data find the cosmic distance duality relation consistent with observations within 1 sigma and no evidence of violation.
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Exploring the interplay of late-time dynamical dark energy and new physics before recombination
Under standard recombination, phantom-crossing dynamical dark energy is preferred at ~97–98.5% probability; early-time fixes to the Hubble tension erase that preference while creating severe ω_m tension with CMB.
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Running into tension: primordial black holes from ultra-slow-roll inflation, spectral running, and the Hubble tension
EDE models increase inferred α_s from CMB data, strengthening tension with USR PBH models that predict negative running.
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Signatures of Modified Gravity on Linear Scales in a Dynamical Dark Energy Background
Using Planck, DESI, supernovae, and redshift-space distortions, the authors infer that modified gravity, if present, must act only below ~30 Mpc and cannot modify the large scales previously considered.
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Cosmological Impact of Redshift-Dependent Type Ia Supernovae Calibration
A phenomenological redshift-dependent SNIa magnitude correction shows no evidence in ΛCDM but is preferred at 4.3σ with dynamical dark energy, reducing Hubble tension to 1.5σ.
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Cosmological Viability of Exponential Infrared $f(T)$ Gravity
Exponential IR f(T) gravity Model I alleviates Hubble tension but is disfavoured by combined Planck/ACT/SPT+DESI+Pantheon+ data; Model II is ruled out because background constraints force unphysical shifts in CMB parameters.
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What it takes to solve the Hubble tension through Modifications of Cosmological Recombination II: in light of ACT DR6 and DESI DR2
Perturbative modifications to the electron mass m_e(z) resolve the Hubble tension with Planck+ACT CMB data but cannot when DESI DR2 BAO data are added due to lowered Omega_m.
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Updates on dipolar anisotropy in local measurements of the Hubble constant from Cosmicflows-4
Local Hubble constant anisotropy in Cosmicflows-4 data is primarily attributed to peculiar velocities and survey structure rather than cosmic-scale isotropy violation, with limited implications for the Hubble tension.
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Extended Dark Energy analysis using DESI DR2 BAO measurements
Extended analysis of DESI DR2 data confirms robust evidence for dynamical dark energy with phantom crossing preference, stable under parametric and non-parametric modeling.
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The Hubble tension: A decade review
Pure early or late fixes to the Hubble tension are tightly constrained; remaining options are combined early-late interacting dark energy or new physics at the local-to-homogeneous transition.
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Early- and Late-Time Modifications to $\Lambda$CDM: Implications for the Hubble Tension
An extended model with decaying dark matter around equality and w0 dark energy yields H0 ≈ 70 km/s/Mpc from Planck+ACT+DESI data, reducing Hubble tension to ~2.2σ while producing Bayesian evidence comparable to ΛCDM.
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Investigating cosmic distance duality and dark energy evolution through intermediate and high-z probes
No significant violation of the cosmic distance duality relation is detected across multiple parameterizations, with flat cosmologies preferred by model selection.