A 2026 compilation of 88 Hubble-constant (H0) measurements that avoid the sound-horizon scale of the cosmic microwave background (CMB) shows that the classical distance ladder (H0 = 72.73 ± 0.39 km s⁻¹ Mpc⁻¹) disagrees with the aggregate of all distance-ladder-independent, sound-horizon-free methods (H0 = 69.37 ± 0.34 km s⁻¹ Mpc⁻¹) at 6.5σ, reduced to 3.9σ under modeled correlations, and that local probes analyzed assuming a ΛCDM expansion history recover H0 about 3.4 km s⁻¹ Mpc⁻¹ lower than cosmological-model-independent analyses of comparable data (2.9σ internal tension). The open problem is to determine the root cause of this 'distance ladder versus the rest' discrepancy: identify and quantify a coherent systematic (in ladder calibrators or in the model-independent methods) that accounts for the required shift; or construct a concrete departure from the standard cosmological model (ΛCDM: cold dark matter plus a cosmological constant) at redshifts below z ~ 1 that reproduces the observed magnitude and redshift dependence of the inferred H0 shifts while remaining consistent with Type Ia supernova, baryon-acoustic-oscillation (including sound-horizon-free), structure-growth, and CMB constraints; or quantify a hybrid of the two. As of August 2026 this remains open: Cepheid crowding systematics have been rejected at high confidence, community-consensus local determinations remain near 73.5, alternative calibrations persist near 70, and proposed early- or late-time modifications alleviate but do not close the gap.

Background

The Hubble constant H0 sets the present-day expansion rate of the universe. In the standard cosmological model (ΛCDM: cold dark matter plus a cosmological constant Λ), H0 is precisely inferred from the cosmic microwave background (CMB) measured by Planck, giving about 67.4 km s⁻¹ Mpc⁻¹. Locally, H0 is measured with a 'distance ladder': nearby geometric anchors (parallaxes from the European Space Agency's Gaia astrometry satellite, water-maser distances to the galaxy NGC 4258, eclipsing binaries in the Large Magellanic Cloud) calibrate Cepheid variable stars (pulsating supergiants with a tight period–luminosity relation), which calibrate Type Ia supernovae (SNe Ia), whose standardizable brightness fixes the distance-redshift relation. The SH0ES team (Supernovae H0 for the Equation of State) built this Cepheid–SN Ia ladder, which gives H0 = 73.04 ± 1.04 km s⁻¹ Mpc⁻¹ (Riess et al. 2022), a roughly 5σ discrepancy with Planck — the Hubble tension, usually framed as an 'early universe versus late universe' split. A leading class of proposed solutions (e.g. early dark energy) reduces the sound horizon r_d, the comoving size of the baryon-acoustic-oscillation (BAO) feature — sound waves in the pre-recombination photon–baryon plasma — which raises the H0 inferred from CMB and BAO data. This motivates measurements that are independent of the sound-horizon scale: if the tension persists even in sound-horizon-free (SHF) determinations, early-universe modifications alone cannot be the whole story. SHF 'one-step' methods bypass the ladder entirely: time-delay cosmography of strongly lensed quasars and supernovae (comparing arrival times of multiple images, which depend on absolute distance), geometric distances to circumnuclear water-maser disks resolved by very-long-baseline interferometry (VLBI; 'megamasers'), gravitational-wave standard sirens (binary-merger waveforms give absolute luminosity distances), the tailored Expanding Photosphere Method (EPM) on Type II supernovae (comparing photospheric angular size with expansion velocity), fast radio bursts, and distance indicators calibrated without reference to CMB physics. Pantos and Perivolaropoulos (2026) compiled 88 such measurements and split them into four categories: (1) Distance Ladder (Cepheids, the tip of the red giant branch (TRGB, a stellar-population distance indicator), J-region asymptotic giant branch (JAGB) carbon stars, and Mira long-period variables calibrating SNe Ia); (2) Local ΛCDM (ladder-independent probes whose analysis assumes the ΛCDM expansion history, e.g. standard siren and standard time-delay analyses); (3) Pure Local (cosmological-model-independent, needing no H(z) shape); and (4) CMB sound-horizon-free analyses. Their headline results are: the 30 ladder measurements give 72.73 ± 0.39; the 58 ladder-independent SHF measurements give 69.37 ± 0.34 (6.5σ apart, 3.9σ after modeling uniform intra-category correlations); Category 2 gives 67.61 ± 0.96 and Category 3 gives 71.03 ± 0.69, a 2.9σ internal offset of about 3.4 km s⁻¹ Mpc⁻¹; and the distribution of the ladder-independent, sound-horizon-free (one-step) measurements shows a possible bimodality, with peaks near the Category 2 (~67.6) and Category 3 (~71.0) values, that rests on a small number of very precise anchors. The authors conclude the tension is better described as 'distance ladder versus the rest' than as early-versus-late, and enumerate what would resolve it: a specific coherent systematic identified and quantified; or a physical model producing late-time (z below ~1) departures from ΛCDM of the right magnitude and redshift dependence, passing all other probes and yielding falsifiable predictions for the Dark Energy Spectroscopic Instrument (DESI) survey, the James Webb Space Telescope (JWST), the LIGO/Virgo/KAGRA gravitational-wave detector network during its O4–O5 observing runs, and the Atacama Cosmology Telescope Data Release 6 (ACT DR6); or a quantified hybrid (e.g. a ~2% ladder calibration error plus a smaller late-time modification).

Problem Statement

Determine the root cause of the discrepancy between distance-ladder determinations of H0 (≈ 72.7 km s⁻¹ Mpc⁻¹) and the aggregate of distance-ladder-independent, sound-horizon-free determinations (≈ 69.4 km s⁻¹ Mpc⁻¹; 6.5σ, or 3.9σ under modeled correlations, per the 88-measurement compilation of Pantos & Perivolaropoulos 2026) — i.e., decide among three explanations and support the decision quantitatively: (a) an unrecognized, coherent systematic affecting either multiple ladder calibrators and standardization steps or the model-independent methods (Cepheid period–luminosity metallicity dependence, common SNe Ia standardization biases) — identify it, demonstrate it with independent data, and show that correcting it closes (or bounds) the gap; or (b) a genuine departure from ΛCDM modifying the true expansion history H(z) at redshifts below z ~ 1 — construct a concrete physical model that reproduces the observed magnitude and redshift dependence of the inferred H0 shifts across the measurement categories without violating constraints from SNe Ia, BAO (including sound-horizon-free BAO), structure growth, and CMB angular power spectra, and that yields testable predictions (e.g. in growth rate or distance ratios) for DESI, JWST, LIGO/Virgo/KAGRA O4–O5, and ACT DR6 data; or (c) a hybrid of both, with each component's contribution quantified. Related supporting analyses discussed in the source, each of which would represent partial progress toward the root-cause identification rather than a complete answer on its own, include: adjudicating whether the ~2.9σ internal offset between ΛCDM-assumed and model-independent local analyses reflects a bias induced by imposing the ΛCDM expansion history or larger unaccounted systematics in model-independent methods (e.g. via larger megamaser samples at z ≳ 0.05, expanded tailored-EPM SNe II samples, and GW bright/dark sirens analyzed both model-dependently and model-independently); establishing whether the distance-ladder-independent, sound-horizon-free one-step H0 distribution is genuinely bimodal or a single broad distribution, which currently rests on a small number of very precise anchors dominating the aggregate; and constructing a full first-principles covariance matrix for the compiled ensemble (tracking shared calibrators, overlapping sample membership, and common pipelines) to make the tension significance definitive. The problem is answered when the root cause is identified with quantitative support satisfying the branch-specific consistency requirements stated above — not by any single intermediate deliverable alone.

References

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