The DM distribution of unlocalized FRBs yields H0 = 73.8 +14.0/-12.3 km/s/Mpc with 18% uncertainty.
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In the Realm of the Hubble tension $-$ a Review of Solutions
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abstract
The $\Lambda$CDM model provides a good fit to a large span of cosmological data but harbors areas of phenomenology. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the $4-6\sigma$ disagreement between predictions of the Hubble constant $H_0$ by early time probes with $\Lambda$CDM model, and a number of late time, model-independent determinations of $H_0$ from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demand a hypothesis with enough rigor to explain multiple observations--whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. We present a thorough review of the problem, including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions. Some of the models presented are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within $1-2\sigma$ between {\it Planck} 2018, using CMB power spectra data, BAO, Pantheon SN data, and R20, the latest SH0ES Team measurement of the Hubble constant ($H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68\% confidence level). Reduced tension might not simply come from a change in $H_0$ but also from an increase in its uncertainty due to degeneracy with additional physics, pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.[Abridged]
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representative citing papers
Pseudo double-source plane lenses enable statistical strong lensing tomography that forecasts σ(w0) ~ 0.45 from the LSST 10-year photometric sample in flat w0waCDM cosmology.
Derives idealized P-L-T relation from hydrostatic envelope model for LRDs and uses sparse data to obtain preliminary H0 = 120.7 with large errors as proof-of-concept.
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.
DESI DR2 BAO data exhibits 2.3 sigma tension with CMB in Lambda-CDM but prefers evolving dark energy (w0 > -1, wa < 0) at 3.1 sigma with CMB and 2.8-4.2 sigma when including supernovae.
First-year DESI BAO data are consistent with flat LambdaCDM and, when combined with CMB, show a 2.5-3.9 sigma preference for evolving dark energy (w0 > -1, wa < 0) that strengthens with certain supernova datasets.
Λ_s VCDM is a predictive model combining Λ_s CDM with VCDM gravity via an auxiliary scalar field and sigmoid-smoothed potentials to enable stable mirror AdS-to-dS transitions with possible transient acceleration.
Cross-correlations of SN Ia in redshift and distance space with galaxies can constrain a constant magnitude offset ΔM at the ~0.05 level in optimistic survey forecasts, partially breaking the H0–ΔM degeneracy.
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.
Assuming τ=0.11±0.006 yields a 2σ positive neutrino mass detection (Σmν=0.10^{+0.04}_{-0.05} eV) and removes CMB-DESI tensions within ΛCDM.
HIcosmo is a new JAX-based differentiable framework for background cosmology inference that matches Cobaya results while delivering 8.7x CPU and up to 20x GPU speedups.
A generalized Chaplygin-type solid unifies dark matter and dark energy via an early pressureless phase transitioning to a late solid phase that supports acceleration and produces distinct low-redshift perturbation signatures.
Using simultaneous modeling of continuum lag-spectrum and broadband SED of Fairall 9 with the H0RIZON-AGN model, the authors obtain H0 = 72.4_{-3.7}^{+3.4} km s^{-1} Mpc^{-1}.
First multiband P-L relations for Cepheids in S-PLUS system with reddening maps of the Magellanic Clouds from single-epoch photometry.
Four BAO-based estimators of the sound-horizon ratio r_d/r_d^fid, each built on a different subset of assumptions (distance duality, flatness, standard ruler), all agree on a single redshift-independent value with current DESI DR2 + Pantheon+ + CC data.
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.
Strong lensing of MBHBs produces identifiable beat patterns in about 7% of detectable two-image LISA events, with Bayesian inference recovering time delay and magnification parameters.
N-body simulations of IDE with Q=ξHρ_x show scale-dependent deviations in the matter power spectrum, density morphology, and halo abundance that standard ΛCDM-calibrated prescriptions cannot reproduce.
Extended misalignment for axion-like particles with constant-ω_ϕ pre-oscillation and dark radiation coupling yields data-driven constraints favoring negative ω_ϕ and f_ϕ in [80, 1.5×10^10] TeV but does not ease cosmological tensions.
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.
An analytic bound on axion parameters in thawing quintessence is derived independently of initial conditions and used with cosmological observations plus quantum gravity constraints to exclude large regions of axion dark energy parameter space.
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.
citing papers explorer
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Dispersion Measure Distribution of Unlocalized Fast Radio Bursts as a Probe of the Hubble Constant
The DM distribution of unlocalized FRBs yields H0 = 73.8 +14.0/-12.3 km/s/Mpc with 18% uncertainty.
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Strong Lensing Tomography: Double and pseudo multi-source plane strong gravitational lensing to constrain dark energy
Pseudo double-source plane lenses enable statistical strong lensing tomography that forecasts σ(w0) ~ 0.45 from the LSST 10-year photometric sample in flat w0waCDM cosmology.
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Little red dots as a cosmological probe: constraining $H_0$ with quasi-periodic pulsations
Derives idealized P-L-T relation from hydrostatic envelope model for LRDs and uses sparse data to obtain preliminary H0 = 120.7 with large errors as proof-of-concept.
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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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DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints
DESI DR2 BAO data exhibits 2.3 sigma tension with CMB in Lambda-CDM but prefers evolving dark energy (w0 > -1, wa < 0) at 3.1 sigma with CMB and 2.8-4.2 sigma when including supernovae.
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DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
First-year DESI BAO data are consistent with flat LambdaCDM and, when combined with CMB, show a 2.5-3.9 sigma preference for evolving dark energy (w0 > -1, wa < 0) that strengthens with certain supernova datasets.
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$\Lambda_{\rm s}$CDM cosmology from a type-II minimally modified gravity
Λ_s VCDM is a predictive model combining Λ_s CDM with VCDM gravity via an auxiliary scalar field and sigmoid-smoothed potentials to enable stable mirror AdS-to-dS transitions with possible transient acceleration.
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Skipping the rungs! Calibrating distance indicators through their clustering with galaxies
Cross-correlations of SN Ia in redshift and distance space with galaxies can constrain a constant magnitude offset ΔM at the ~0.05 level in optimistic survey forecasts, partially breaking the H0–ΔM degeneracy.
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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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Cosmological Concordance in an Especially Opaque Universe: A Tentative Cosmological Detection of Physical Neutrino Mass in $\Lambda$CDM
Assuming τ=0.11±0.006 yields a 2σ positive neutrino mass detection (Σmν=0.10^{+0.04}_{-0.05} eV) and removes CMB-DESI tensions within ΛCDM.
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HIcosmo: a differentiable JAX-based framework for cosmology inference
HIcosmo is a new JAX-based differentiable framework for background cosmology inference that matches Cobaya results while delivering 8.7x CPU and up to 20x GPU speedups.
-
A solid unification of the dark sector
A generalized Chaplygin-type solid unifies dark matter and dark energy via an early pressureless phase transitioning to a late solid phase that supports acceleration and produces distinct low-redshift perturbation signatures.
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HALO II: Constraining Hubble constant $H_{0}$ through continuum delay fitting of Fairall 9
Using simultaneous modeling of continuum lag-spectrum and broadband SED of Fairall 9 with the H0RIZON-AGN model, the authors obtain H0 = 72.4_{-3.7}^{+3.4} km s^{-1} Mpc^{-1}.
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Variables in S-PLUS: I. Multiband period-luminosity relations and reddening maps of the Magellanic Clouds using classical Cepheids
First multiband P-L relations for Cepheids in S-PLUS system with reddening maps of the Magellanic Clouds from single-epoch photometry.
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The cosmic tetrarchy: four estimators breaking the assumption degeneracy in cosmological distance tensions
Four BAO-based estimators of the sound-horizon ratio r_d/r_d^fid, each built on a different subset of assumptions (distance duality, flatness, standard ruler), all agree on a single redshift-independent value with current DESI DR2 + Pantheon+ + CC data.
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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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Identification of Lensed Gravitational-Wave Beat Patterns by LISA
Strong lensing of MBHBs produces identifiable beat patterns in about 7% of detectable two-image LISA events, with Bayesian inference recovering time delay and magnification parameters.
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Non-linear Structure Formation in Planck+DESI Favoured Interacting Dark Energy Cosmologies
N-body simulations of IDE with Q=ξHρ_x show scale-dependent deviations in the matter power spectrum, density morphology, and halo abundance that standard ΛCDM-calibrated prescriptions cannot reproduce.
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Axion dark matter from extended misalignment with a constant-$\omega_\phi$ pre-oscillatory phase and dark radiation
Extended misalignment for axion-like particles with constant-ω_ϕ pre-oscillation and dark radiation coupling yields data-driven constraints favoring negative ω_ϕ and f_ϕ in [80, 1.5×10^10] TeV but does not ease cosmological tensions.
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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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Bounding axion dark energy
An analytic bound on axion parameters in thawing quintessence is derived independently of initial conditions and used with cosmological observations plus quantum gravity constraints to exclude large regions of axion dark energy parameter space.
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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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Sign-Switching Dark Energy: Smooth Transitions with Recent DESI DR2 Observations
Sign-switching dark energy with a transition at z_† fits recent DESI DR2, Planck CMB, and Pantheon+ data better than ΛCDM while raising the inferred Hubble constant and easing the Hubble tension.
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Evidence for deviation in gravitational light deflection from general relativity at cosmological scales with KiDS-Legacy and CMB lensing
KiDS-Legacy weak lensing plus CMB data yields a 3 sigma deviation in light deflection from GR in a Lambda CDM background, with the signal driven by large-scale CMB lensing amplitudes.
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Nonlinear Matter Power Spectrum from relativistic $N$-body Simulations: $\Lambda_{\rm s}$CDM versus $\Lambda$CDM
Relativistic N-body simulations of Lambda_s CDM produce a redshift-dependent crest in the matter power spectrum ratio, peaking at 20-25% near the transition and leaving a 15-20% uplift at z=0 on group scales.
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Connecting Early Dark Energy to Late Dark Energy by the Diluting Matter Potential
A scale-invariant model uses a diluting-matter-dependent potential to connect early and late dark energy via tunneling, alleviating the Hubble tension with best-fit early dark energy fraction ~0.3 at z~5000.
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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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Spherical Collapse and Halo Formation in a Cosmology with Decaying Dark Matter and a Semi-Cosmographic Dark Energy
In a decaying dark matter plus semi-cosmographic dark energy cosmology constrained by DESI BAO and ShapeFit, the spherical collapse threshold stays close to the ΛCDM value while massive halo abundance shows pronounced deviations that enable joint constraints on DDM lifetime and dark energy parameter
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An Interplay Between Fractional Calculus and Holographic Dark Energy
Introduces Fractional Holographic Dark Energy (FHDE) via fractionally corrected entropy from a modified Wheeler-DeWitt equation and studies its late-time cosmology, field reconstructions, and extensions to modified gravity theories.
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Evolving Dark Energy Is Vacuum Energy After All
A QCD-vacuum dark-energy model with a two-parameter switch reproduces the DESI-preferred late-time expansion and is mildly favoured over ΛCDM by Bayesian evidence (lnB≈2.7).
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Impact of inhomogeneous curvature on growth rate measurements from magnitude fluctuations
Full-GR simulations find that inhomogeneous curvature produces only sub-dominant systematic offsets in growth-rate measurements from magnitude fluctuations at z ≲ 0.2 relative to current statistical errors.
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The DESI results impact the local determination of $H_0$
Reanalysis shows DESI-preferred w0wa models reduce local H0 by 0.5-2.5 km s^{-1} Mpc^{-1} relative to LambdaCDM.
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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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Towards a causal effective thermodynamics of scalar-tensor gravity
A causal Israel–Stewart extension of scalar-tensor thermodynamics is constructed via a timelike heat-flux ansatz, enabling the first explicit split of K and T in Bianchi I and FLRW universes.
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Constraints on Schwarzschild Black Hole in a Generalized Dehnen-Type $(1,4,\gamma)$ Dark Matter Halo via the S2 Star Orbit around Sgr A$^\star$
Derives perihelion shift equations for S2 star in generalized Schwarzschild-Dehnen BH-DM spacetime and constrains gamma, rho_s, rs via MCMC on Do et al. and Gillessen et al. datasets.
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Negative neutrino mass or negative dark energy?
A sign-switching dark energy model (Λ_s CDM) recovers positive effective neutrino masses (0.055 ± 0.050 eV) consistent with oscillation data, unlike ΛCDM which prefers negative values (-0.075 eV), for DESI DR2 + CMB + supernova fits with z_† > 2.4.
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Study of dark interactions through strong gravitational lenses
Strong gravitational lensing data from early-type galaxies and Abell 1689 constrain three sign-changeable dark-sector interaction models, yielding negative interaction strengths larger in magnitude than prior probes and an acceleration transition at z_t ~1.8-2.1.
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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.
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Do equation of state parametrizations of dark energy faithfully capture the dynamics of the late universe?
Node-based reconstruction of cosmic expansion prefers stronger deceleration at z≈1.7 than smooth DE EoS parametrizations, isolating z~1.5-2 as a window where the latter may compress localized kinematic features permitted by current data.
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Measuring neutrino mass in light of ACT DR6 and DESI DR2
New ACT and DESI data yield model-dependent upper limits on sum of neutrino masses, with holographic dark energy giving the tightest bounds and a consistent preference for degenerate hierarchy.
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New constraints on cosmic anisotropy from galaxy clusters using an improved dipole fitting method
Galaxy cluster observations yield two preferred directions with cosmic anisotropy amplitude of about 5.3 times 10 to the minus 4 at roughly 1 sigma overall significance, though higher in the XMM-Newton subsample.
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Revisiting the Matter Creation Process: Observational Constraints on Gravitationally Induced Dark Energy and the Hubble Tension
Gravitationally induced particle creation models fit cosmological data as well as ΛCDM and reduce the Hubble tension from 4.3σ to 2.4–3σ.
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Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity
The w†VCDM model shows a statistically significant preference for late-time quintessence-phantom crossing dark energy, raises the Hubble constant, and satisfies neutrino mass and Neff constraints from current cosmological datasets.
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Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model
Nonminimal curvature-matter coupling produces dynamical dark energy consistent with DESI observations and lunar laser ranging equivalence principle constraints.
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Nearly Degenerate Majorana Dark Matter and Its Self-Interactions in a Gauged $U(1)_{L_\mu - L_\tau}$ Model
A gauged U(1)_{Lμ-Lτ} model generates nearly degenerate Majorana dark matter whose self-interactions via a light scalar mediator set the relic density, resolve core-cusp anomalies, and fit LZ direct detection plus muon g-2 bounds.
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The implications of inflation for the last ACT
A parameterized slow-roll model and a new exponential f(R) inflation model are constrained by P-ACT-LB-BK18 data, with the latter aligning to the ACT scalar spectral index preference in both standard and EDE frameworks.
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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.
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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.