Current State

The H₀ tension has reached its most acute level to date. As of the 2025 Corfu conference, the discrepancy between early- and late-Universe determinations of the Hubble constant has exceeded 6σ significance, with contributions from DESI, JWST, and ACT making the tension more robust rather than dissolving it [AG-2025.09-614]. The canonical conflict pits the CMB-inferred value (Planck, ~67 km/s/Mpc) against the local distance-ladder value anchored by Cepheids and SH0ES (~73 km/s/Mpc), a ~5σ discrepancy also confirmed through binned supernova analyses [AG-2025.01-248]. Crucially, nonparametric reconstruction of the late-time expansion history using DESI BAO and PantheonPlus data reveals a "sound horizon tension" at the 5σ level when the SH0ES H₀ prior is applied, and identifies non-monotonic features—a bump at z ~ 0.5 and a depression at z ~ 0.9—that are inconsistent with a simple w₀wₐCDM fit and absent from older SDSS measurements [AG-2024.08-072]. This hints that DESI data itself may encode new structural information about dark energy.

Key Approaches

Modified gravity frameworks have been extensively tested against DESI DR2 data. Teleparallel Gauss-Bonnet gravity, defined through the torsion scalar T and torsion-based Gauss-Bonnet invariant T_G, partially alleviates the tension, returning H₀ estimates of 69–71.5 km/s/Mpc and an effective equation of state ω_eff(z=0) ≈ −0.664 to −0.693 [AG-2026.01-318]. A more radical geometric approach proposes building cosmological models from spaces with intrinsic rather than explicit symmetries, showing that a Hubble tension arises naturally within this framework and that its BAO predictions are consistent with DESI Y1 data [AG-2024.04-241].

Dark energy model building has focused on holographic dark energy (HDE). A systematic study across six HDE models using DESI DR2 BAO, Planck 2018 CMB priors, and three SN Ia compilations finds that models using the Hubble scale as infrared cutoff fail to alleviate the tension, while those using the future event horizon as cutoff achieve only partial mitigation—a conclusion robust across different datasets [AG-2025.11-263]. Similarly, HDE embedded in Unimodular Gravity, tested against cosmic chronometers, Pantheon+SH0ES, DESI DR2 BAO, and Planck CMB, does not alleviate the tension and is not preferred by Bayesian evidence over ΛCDM [AG-2025.08-588].

Cosmographic and observational diagnostics reveal that the standard flat-ΛCDM model cannot simultaneously accommodate high-redshift Planck constraints and local Cepheid measurements; tension becomes pronounced only when both priors are applied jointly, and worsens when LRG1 and LRG2 DESI tracers are excluded [AG-2024.08-317]. High-redshift probes including GRBs and quasars extend the Hubble diagram and show a decreasing trend of H₀ with redshift, with evolutionary coefficient η ~ 0.01 [AG-2025.01-248].

Novel null tests offer a path forward. A proposed geometric test combines strong-lensing time-delay distances with gravitational-wave standard-siren luminosity distances into an H₀-independent dimensionless ratio, enabling unambiguous discrimination between early- and late-Universe origins of the tension without relying on the distance ladder or the sound horizon [AG-2026.01-590].

Open Problems

The core ambiguity—whether the tension originates from pre-recombination new physics, late-time modifications, or systematic errors—remains unresolved [AG-2025.09-614, AG-2026.01-590]. The nonparametric reconstruction study explicitly concludes that the 5σ sound horizon tension reinforces the need for pre-recombination new physics [AG-2024.08-072]. Meanwhile, the role of look-back time and multi-redshift calibration methods as alternative resolution pathways remains underexplored [AG-2024.03-270]. The S₈ tension and emerging anomalies related to dynamical dark energy and neutrino physics add further complexity, suggesting that any resolution of H₀ alone may be insufficient [AG-2025.09-614].

Where to Read Next

For a comprehensive community assessment incorporating DESI and JWST data, see [AG-2025.09-614]. For detailed nonparametric expansion history reconstruction and sound horizon tension quantification with DESI DR2, see [AG-2024.08-072]. The novel null-test framework using gravitational-wave sirens is developed in [AG-2026.01-590], and the most systematic HDE survey against DESI DR2 is in [AG-2025.11-263].