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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The Hubble Hunter's Guide
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abstract
Measurements of the Hubble constant, and more generally measurements of the expansion rate and distances over the interval $0 < z < 1$, appear to be inconsistent with the predictions of the standard cosmological model ($\Lambda$CDM) given observations of cosmic microwave background temperature and polarization anisotropies. Here we consider a variety of types of departures from $\Lambda$CDM that could, in principle, restore concordance among these datasets, and we explain why we find almost all of them unlikely to be successful. We single out the set of solutions that increase the expansion rate in the decade of scale factor expansion just prior to recombination as the least unlikely. These solutions are themselves tightly constrained by their impact on photon diffusion and on the gravitational driving of acoustic oscillations of the modes that begin oscillating during this epoch -- modes that project on to angular scales that are very well measured. We point out that a general feature of such solutions is a residual to fits to $\Lambda$CDM, like the one observed in Planck power spectra. This residual drives the modestly significant inferences of angular-scale dependence to the matter density and anomalously high lensing power, puzzling aspects of a data set that is otherwise extremely well fit by $\Lambda$CDM.
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representative 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.
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.
Combining GWTC-4 standard sirens with TDCOSMO2025 lensing data under the distance sum rule yields H0 = 83.78 +12.53/-10.23 km/s/Mpc (13.6% precision) in one configuration, consistent with both Planck and SH0ES.
New constraints on dark radiation parameters from recent cosmological datasets show the model alleviates the Hubble tension with SH0ES inclusion while remaining consistent with standard expectations without it.
Tensions in the supernova intercept a_B at z~0.01 in PantheonPlus and z~0.1 in DES-Y5 point to data systematics or inter-survey inconsistencies rather than new physics, aligning H0 measurements and reducing support for dynamical dark energy.
Including spectral running α_s, β_s and self-interacting dark radiation relaxes the ACT DR6 bound on ΔN_eff to <0.58 and lowers the Hubble tension to 2.2σ with three extra parameters.
A swampland-inspired DM-EDE coupling is tested against DESI DR2 BAO data, showing the EDE potential construction affects late-time dark energy constraints.
Axion EDE model fitted to Planck/ACT/SPT CMB, DESI BAO, and JWST UV luminosity function data yields H0 = 71.58 ± 1.05 km s^{-1} Mpc^{-1}, reduces H0 tension to 1.0 sigma, and improves Δχ^{2}_tot = -18.26 over Λ CDM.
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.
A 0.19 mag step in supernova absolute magnitude at 20 Mpc improves data fit and increases the Hubble constant by 2% while leaving matter density and dark energy parameters stable.
Two three-parameter extensions of the mAH dark energy parametrization are compared to LambdaCDM, wCDM, CPL and others using CMB, DESI BAO, H(z), RSD and three SNIa samples, yielding Delta chi-squared improvements of 6-38 and 2-5 sigma tensions with LambdaCDM.
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.
Bulk viscous fluid models for dark energy yield improved fits to supernova, BAO, and CMB data over LambdaCDM, especially in the interacting non-minimal case.
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.
MCMC constraints on two Lambda(t) models with DESI DR2, CC, and Pantheon+ data yield H0 ~72.5-73 km/s/Mpc, Omega_m0 near standard values in joint fits, and n~0.3 indicating mild deviation from LambdaCDM.
The Hubble tension between local and early-universe expansion-rate measurements may be resolved by early dark energy that speeds up expansion before recombination while satisfying existing constraints.
A review summarizing the Hubble constant tension and proposed solutions from new physics that restore agreement between Planck CMB data and local H0 measurements within 1-2 sigma.
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.
-
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.
-
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.
-
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.
-
Model-independent H0 from GWTC-4 standard sirens and TDCOSMO 2025 strong lensing time delays
Combining GWTC-4 standard sirens with TDCOSMO2025 lensing data under the distance sum rule yields H0 = 83.78 +12.53/-10.23 km/s/Mpc (13.6% precision) in one configuration, consistent with both Planck and SH0ES.
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Exploring the Dark Sector: Interacting Radiation in Light of Modern Cosmological Probes
New constraints on dark radiation parameters from recent cosmological datasets show the model alleviates the Hubble tension with SH0ES inclusion while remaining consistent with standard expectations without it.
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Cosmological intercept tension
Tensions in the supernova intercept a_B at z~0.01 in PantheonPlus and z~0.1 in DES-Y5 point to data systematics or inter-survey inconsistencies rather than new physics, aligning H0 measurements and reducing support for dynamical dark energy.
-
The End of the First Act: Spectral Running, Interacting Dark Radiation, and the Hubble Tension in Light of ACT DR6 Data
Including spectral running α_s, β_s and self-interacting dark radiation relaxes the ACT DR6 bound on ΔN_eff to <0.58 and lowers the Hubble tension to 2.2σ with three extra parameters.
-
Imprint of swampland-inspired coupled early dark energy
A swampland-inspired DM-EDE coupling is tested against DESI DR2 BAO data, showing the EDE potential construction affects late-time dark energy constraints.
-
Resolving the Hubble Tension in the Early Dark Energy Framework with JWST and DESI Data
Axion EDE model fitted to Planck/ACT/SPT CMB, DESI BAO, and JWST UV luminosity function data yields H0 = 71.58 ± 1.05 km s^{-1} Mpc^{-1}, reduces H0 tension to 1.0 sigma, and improves Δχ^{2}_tot = -18.26 over Λ CDM.
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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.
-
Impact of the SNe Ia Magnitude Transition at 20 Mpc on Cosmological Parameter Estimation
A 0.19 mag step in supernova absolute magnitude at 20 Mpc improves data fit and increases the Hubble constant by 2% while leaving matter density and dark energy parameters stable.
-
Beyond CPL: Evidence for dynamical dark energy in three-parameter models
Two three-parameter extensions of the mAH dark energy parametrization are compared to LambdaCDM, wCDM, CPL and others using CMB, DESI BAO, H(z), RSD and three SNIa samples, yielding Delta chi-squared improvements of 6-38 and 2-5 sigma tensions with LambdaCDM.
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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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Dissipative Cosmology and the Nature of Dark Energy: Insights from Bulk Viscosity with DESI DR2 observations
Bulk viscous fluid models for dark energy yield improved fits to supernova, BAO, and CMB data over LambdaCDM, especially in the interacting non-minimal case.
-
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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Observational tests of \texorpdfstring{$\Lambda(t)$}{Lambda(t)} cosmology in light of DESI DR2
MCMC constraints on two Lambda(t) models with DESI DR2, CC, and Pantheon+ data yield H0 ~72.5-73 km/s/Mpc, Omega_m0 near standard values in joint fits, and n~0.3 indicating mild deviation from LambdaCDM.
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The Hubble Tension and Early Dark Energy
The Hubble tension between local and early-universe expansion-rate measurements may be resolved by early dark energy that speeds up expansion before recombination while satisfying existing constraints.
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In the Realm of the Hubble tension $-$ a Review of Solutions
A review summarizing the Hubble constant tension and proposed solutions from new physics that restore agreement between Planck CMB data and local H0 measurements within 1-2 sigma.