PRESS RELEASE August 2026 — The Hubble Tension May Not Be a Disagreement About Expansion, But a Disagreement About Rulers – Institute of Integrative and Interdisciplinary Research

TORONTO, ON, August 2026 — The Hubble Tension May Not Be a Disagreement About Expansion, But a Disagreement About Rulers

Three new studies from the Institute of Integrative and Interdisciplinary Research propose that the decade-long conflict between early- and late-universe measurements of the Hubble constant is not a failure of cosmology but a property of the objects used to calibrate it. Galaxies, supernovae, and their host structures are embedded in the cosmic web — and the web, being permeable and only partially coupled to expansion, lags behind the background. A ruler that lags is a ruler that is short. A short ruler makes distances look smaller and the expansion rate look larger. The size of the lag is not fitted: it is computed from nucleon sigma terms and the mass fraction of matter in the web, and it agrees with two independently anchored measurements.

The three preprints:

Cosmic Web Lag as the Possible Origin of the Hubble Tension: Separating Directional Anisotropy from Anchor Bias. https://doi.org/10.13140/RG.2.2.12054.92481
Two Channels for One Coupling: A Boltzmann Test of the QCD Vacuum–Matter Coupling and the Slippage Origin of the Factor 1.65. https://doi.org/10.13140/RG.2.2.15017.15204
Rulers Woven into the Web: Three Convergent Determinations of the Cosmic Web Lag. https://doi.org/10.13140/RG.2.2.19932.35202

The problem, restated.

For a decade, two classes of measurement have disagreed about how fast the universe expands. The cosmic microwave background gives 67.4 km/s/Mpc. The distance ladder gives 73.0. The gap is roughly 8% and has survived every attempt to attribute it to a single instrument or a single team. The standard framing treats this as a question about epoch — the early universe against the late universe.

The first of the three new papers argues that the question has been posed along the wrong axis, and that in fact there are two independent axes. One is direction: whether expansion is anisotropic, a quadrupolar question addressed by shear, bulk flows, and polarization. The other is anchor: what a given determination is calibrated against. The paper proves the two axes orthogonal — an anchor bias is exactly isotropic and cannot masquerade as anisotropy, and no amount of anisotropy can produce a uniform offset in a calibration chain. Almost all the observational effort of the past decade has gone into the first axis. The second has been left largely unexamined.

The paper then closes the first axis quantitatively within the αLGQV framework. Taking the shear entry as computed rather than assumed, the framework yields a present-day shear density Ω_σ0 ≈ 10⁻⁵⁶ and a distance-modulus quadrupole of 7.6 × 10⁻²⁸ magnitudes — sixteen orders of magnitude below the nucleosynthesis ceiling and twenty-six orders below what a shear-only resolution of the tension would require. The anisotropy route is not merely disfavoured; within this framework it is structurally empty. A parity-based ledger separates the remaining anisotropy channels into three — tensor shear, scalar modulation, and pseudoscalar chirality — and identifies the CMB EB correlation as the unique clean instrument for the third. That entry too is computed and found to be 10⁸ below current birefringence sensitivity. The forecast is negative, and is published as negative.

Why the web lags: the third regime.

Matter in the universe is usually treated as belonging to one of two regimes. Virialized objects — galaxies, clusters — have decoupled from expansion entirely and do not grow. Free comoving matter expands exactly with the background. The cosmic web belongs to neither. It is a percolating, permeable structure that does expand, but more slowly than the background, because a fraction of the momentum flux that would carry it outward is intercepted by the matter woven into it.

An earlier image used in the programme — a tablecloth carrying dishes — was discarded, because a cloth is impermeable and gives the wrong sign twice. The correct image is a string bag: an avos’ka. The mesh stretches, but what passes through the holes is what makes the stretching incomplete. Permeability is the essential feature, not an incidental one.

From this the sign follows without ambiguity. If the web lags by a fraction ε, the calibration ruler embedded in it is short by ε, distances inferred with that ruler are underestimated, and the Hubble constant is correspondingly overestimated:

H_inferred / H_background = 1 / (1 − ε)

The lag is computed, not fitted.

The interception relation gives ε as the product of two quantities, neither of them cosmological:

ε = (σ / m_N) · f_web = 0.0959 × 0.85 = 0.0815

The first factor is the pion–nucleon sigma term divided by the nucleon mass — the same measured hadronic quantity from which the αLGQV programme derives the cosmological constant. The second is the fraction of cosmic mass residing in walls, filaments, and nodes, taken as 0.85 from published morphological censuses of N-body simulations, which give 0.864. The interception is mass-weighted, not volume-weighted: the connected web occupies about 21% of the volume, and a volume-weighted count gives 0.020, missing by a factor of four.

Neither factor was chosen to fit the Hubble tension. The measured discrepancy, expressed as a lag, is 0.078–0.082.

Where the coupling cannot live.

The second paper is a negative result, obtained deliberately and reported as such. Before the calibration interpretation can be asserted, the two conventional places to put a vacuum–matter coupling must be closed. A species diluting as ρ_m ∝ a^−3(1+α) is formally a fluid with equation of state w = α and vanishing sound speed. The Boltzmann code CLASS was patched to admit this configuration — the guard rejecting positive fluid equations of state was removed — and full lensed spectra were computed.

The perturbation channel is excluded decisively and on directly measured quantities: σ₈ rises to 0.930 against the observed 0.811, and the lensing potential is displaced by 34% rms. The background channel fails for a different reason: it contracts the sound horizon by only a few percent, far short of what low-redshift determinations require, and cannot be driven further without pushing H₀ above any measured value.

Elimination leaves the calibration channel — in which the expansion history is exactly ΛCDM, and the coupling enters nowhere in the dynamics, only in the accounting.

“The result people expected us to want was that the coupling shows up in the Friedmann equation,” said Boris Kriger, Lead Investigator. “It does not. We patched a Boltzmann code specifically to give it every chance, and it failed on σ₈ and on lensing. That is published in full. What survives is less glamorous and, I think, more interesting: the coupling does not change how the universe expands. It changes what our rulers are made of.”

Three rulers, one lag.

The third paper asks whether the lag can be determined more than once, from data with different anchors. It can be, three times:

— Hadronically, from the interception relation: ε = 0.0815, containing no cosmological input at all.

— From the Hubble discrepancy itself: 1 − 67.36/73.04 = 0.0778 ± 0.0131.

— From a lens-anchored sound horizon: Arendse et al. (2019) obtain a sound horizon of 138 ± 5 Mpc from time-delay lensing combined with supernovae and BAO — a chain anchored on time delays rather than Cepheids, and therefore genuinely independent rather than a Hubble ratio in disguise. Against the CMB value of 147.09 ± 0.26 this gives ε = 0.0618 ± 0.0340.

The hadronic value lies 0.3σ from the second and 0.6σ from the third. Adopting it — the determination with no cosmological content — the framework then predicts, with no remaining freedom, a galaxy-frame sound horizon of 135.1 Mpc against the measured 138 ± 5, and a ladder Hubble constant of 73.34 against the measured 73.04 ± 1.04.

Two further consequences follow. The residual factor of approximately 1.65 between the cosmological constant derived from sigma terms and the value inferred from late-time distances — a long-standing loose end in the programme — emerges as slippage: (1 − ε)^−6 = 1.665. The exponent is flagged throughout as declared rather than derived, following the Institute’s own published Code of Practice for introducing entities in cosmology, and the data discriminate it from the competing values n = 7 (off by 10%) and n = 3 (off by 22%). Separately, the coupling constant α is identified as a mixed quantity, α = Ω_b · σ/m_N = 0.00473, already carrying a cosmic abundance factor — which means that substituting α for a per-nucleon coupling, as earlier work in the programme did, was a category error. It is corrected in these papers.

A test that is not circular.

Classifying Hubble determinations by anchor rather than by epoch is, on the familiar probes, degenerate with the standard early/late split. The papers state this explicitly and decline to count it as evidence. The classification becomes non-degenerate on six late-time determinations that are free of the sound horizon: these side with the background group, at a weighted mean of 69.11 — 1.70 from the background prediction against 4.35 from the web-anchored prediction.

One point contradicts. The tip-of-the-red-giant-branch determination, 69.8, is web-anchored by the criterion but sits 4.1 below its class. It is retained in the table as the single contradicting case. An argument that would explain it away is stated in the Discussion and then explicitly not used, because it was formulated after the number was seen.

What would falsify this.

The papers specify concrete refutations. Detection of cosmic shear at the 1% level discussed in the recent literature — Ω_σ0 ≈ 2.5 × 10⁻⁵ — kills the framework outright, since it predicts 10⁻⁵⁶. A determination of the mass fraction of the cosmic web substantially away from 0.85 breaks the interception relation, which has no adjustable factor to absorb it. The sigma term is not free either: because Λ ∼ σ⁷ and H₀ ∼ σ^3.5 in the programme, lowering σ from 90 MeV to 75 MeV to improve the fit to ε would drive H₀ to 38 km/s/Mpc. And sound-horizon-free late-time determinations converging instead on the ladder value would remove the empirical test’s only non-circular support.

What is not claimed.

The papers name their own weak points rather than burying them. The most serious is a possible double count: whether the calibration bias is genuinely independent of the linear perturbative term. The suppression of that term rests on the argument that the percolating web has no exterior within the surveyed volume — the web does not break off, and it does expand, only more slowly. That argument is stated as an argument, not as a proof, and is flagged as potentially fatal. The interception coefficient σ/m_N is a posit. The web mass fraction is an external input inherited from simulations, and therefore carries a weak dependence on the cosmology assumed in those runs — the one respect in which the hadronic determination is not wholly free of cosmological content. Three negative results are published in full: exact scale-invariance of the linking number, which means topology alone cannot produce a lag; the rotational-asymmetry route, which has the right sign but falls short by 12.4 orders of magnitude; and Plateau’s laws, which fix angles rather than thicknesses and so cannot supply the volume fraction.

The framework is also, in part, portable. The sections on the third dynamical regime, on interception, and on the anchor-based empirical test involve no topology and apply to ΛCDM as written. A reader who rejects the RP³ topology may treat ε as a single measured parameter, losing the quantitative agreement but keeping the mechanism, the classification, and the test.

An invitation.

The Institute invites cosmologists, nuclear physicists, and observational scientists to scrutinize, reproduce, and test these results — particularly the interception relation, which requires only a census of cosmic web mass, and the anchor-based classification, which requires only that existing H₀ determinations be re-sorted by what they are calibrated against. Researchers interested in independent implementation, in the double-counting question, or in comparison against forthcoming survey data are invited to contact the Institute directly at boriskriger@interdisciplinary-institute.org

Preprints:

Kriger, B. (2026, August). Cosmic web lag as the possible origin of the Hubble tension: Separating directional anisotropy from anchor bias. IIIR Cosmology and Theoretical Physics. https://doi.org/10.13140/RG.2.2.12054.92481

Kriger, B. (2026, August). Two channels for one coupling: A Boltzmann test of the QCD vacuum–matter coupling and the slippage origin of the factor 1.65. IIIR Cosmology and Theoretical Physics. https://doi.org/10.13140/RG.2.2.15017.15204

Kriger, B. (2026, August). Rulers woven into the web: Three convergent determinations of the cosmic web lag. IIIR Cosmology and Theoretical Physics. https://doi.org/10.13140/RG.2.2.19932.35202

Full αLGQV programme: interdisciplinary-research.institute/cosmology-and-theoretical-physics

Reception and correspondence: interdisciplinary-research.institute/reception

Boris Kriger | Lead Investigator ORCID: orcid.org/0009-0001-0034-2903 Institute of Integrative and Interdisciplinary Research, Toronto +1 437-552-8807 · boriskriger@interdisciplinary-institute.org

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The Institute of Integrative and Interdisciplinary Research (IIIR) is a Toronto-based organization dedicated to solving complex problems through formal precision and cross-domain synthesis. Treating interdisciplinarity as a methodological necessity, the Institute bridges specialized fields to develop coherent theoretical architectures.