Explanation for the Hubble constant tension

Determine the explanation for the more-than-4σ tension between direct measurements of the Hubble constant from Type-Ia supernovae (approximately 72.3 ± 1.4 (stat) ± 1.4 (syst) km s^{-1} Mpc^{-1}) and values inferred from Cosmic Microwave Background anisotropy measurements (approximately 67.4 ± 0.5 km s^{-1} Mpc^{-1}) under the standard ΛCDM cosmological framework.

Background

The paper highlights a major discrepancy—commonly referred to as the Hubble tension—between local determinations of the Hubble constant using Type-Ia supernovae and the value inferred from CMB observations within the ΛCDM model. The authors note that this disagreement exceeds 4σ and explicitly state that its explanation is currently unknown.

Motivated by this unresolved issue, the paper explores a phenomenological extension to ΛCDM via a thermal y-type distortion of the cosmic neutrino background. This distortion effectively increases the relativistic energy density, reducing the sound horizon and permitting higher H0 values, thereby potentially mitigating the tension. Nonetheless, the underlying cause of the tension remains unidentified in the broader cosmological context.

References

The most significant of these is the disagreement between direct measurement of the Hubble Constant $H_0$ using standard candles such as Type-Ia supernovae resulting in a value of $72.3 \pm 1.4\ \mathrm{(stat)}\ \pm 1.4\ \mathrm{(syst)}\ \mathrm{km\ s{-1}\ Mpc{-1}$ , and measurement of $H_0$ obtained from measurements of the anisotropy of the Cosmic Microwave Background, which give a value of $67.4 \pm 0.5 \ \mathrm{km\ s{-1}\ Mpc{-1}$ , resulting in a tension in excess of $4 \sigma$. The explanation for this tension is currently unknown.

— A bound on thermal y-distortion of the cosmic neutrino background  (2407.18102 - Barenboim et al., 2024) in Section 1 (Introduction)

It remains an open question as to whether this tension arises from some unaccounted for systematic error associated with the cosmic distance ladder or intrinsic to SNe Ia themselves, or whether our standard cosmological model -- \LambdaCDM -- is incomplete.

— Weak in the Presence of Beauty: Gravitational waves from the mergers of black holes and neutron stars as a messenger  (2609.16463 - Panther et al., 15 Sep 2026) in Section 7, subsection “Cosmology as population-level inference”

Several issues remain open. Most importantly, the present analysis does not derive the required alignment and multi-harmonic structure from a specific heterotic compactification. Establishing such a construction would provide a microscopic test of the scenario. Likewise, the $10{-28}$ eV sector should ultimately be confronted with the full set of CMB, BAO, supernova, and structure-formation constraints through a numerical cosmological analysis. Such an analysis is necessary to determine quantitatively how large a reduction of the sound horizon can be obtained while remaining consistent with the other cosmological observables.

— Toward a Unified Axion Cosmology  (2608.22667 - Fukuyama, 24 Aug 2026) in Section 4, Discussion and conclusions