In the Realm of the Hubble tension $-$ a Review of Solutions

TL;DR

The paper surveys the persistent H0 tension between early-Universe Planck inferences and late-Universe local measurements, organizing a vast landscape of proposed resolutions into categories such as Early Dark Energy, Late Dark Energy, extra relativistic species, interacting models, unified cosmologies, and modified gravity. It critically assesses how these models affect the sound horizon r_d and the Hubble rate H0, highlighting that many approaches improve individual data fits but often clash with BAO, SNIa, or CMB constraints when analyzed comprehensively. The review emphasizes that no single scenario dominates in likelihood; instead, several avenues—especially dynamic dark energy, dark radiation, and certain modified gravity frameworks—offer the best prospects yet face substantial tests from upcoming observations. The authors advocate for broader, cross-probe measurements and rigorous Bayesian model comparisons to establish a robust cosmological concordance that can accommodate diverse datasets while addressing the H0 discrepancy. Overall, the work underscores the Hubble tension as a potential window into new physics, requiring coordinated theoretical and observational advances to reach a consensus.

Abstract

The $Λ$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 $4-6σ$ disagreement between predictions of the Hubble constant $H_0$ by early time probes with $Λ$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 $1-2σ$ 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]

Figures (19)

• Figure 1: Whisker plot with 68% CL constraints of the Hubble constant $H_0$ through direct and indirect measurements by different astronomical missions and groups performed over the years. The cyan vertical band corresponds to the $H_0$ value from SH0ES Team Riess:2020fzl (R20, $H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68% CL) and the light pink vertical band corresponds to the $H_0$ value as reported by Planck 2018 team Aghanim:2018eyx within a $\Lambda$CDM scenario. A sample code for producing similar figures with any choice of the data is made publicly available online at https://github.com/lucavisinelli/H0TensionRealm.
• Figure 2: Filtered version of Fig. \ref{['fig:H0-CMB-Local']} showing the 68% CL constraints of the Hubble constant $H_0$ with error bars less than $3 {\rm \,km\,s^{-1}\,Mpc^{-1}}$ for the direct measurements and less than $1.5 {\rm \,km\,s^{-1}\,Mpc^{-1}}$ for the indirect estimates. Similar to Fig. \ref{['fig:H0-CMB-Local']}, the cyan vertical band corresponds to the $H_0$ value from SH0ES Team Riess:2020fzl (R20, $H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68% CL) and the light pink vertical band corresponds to the $H_0$ value as reported by Planck 2018 team Aghanim:2018eyx within a $\Lambda$CDM scenario. A dotted vertical line for $H_0= 69.3 {\rm\,km\,s^{-1}\,Mpc^{-1}}$ has been added for a quick visualization of the division for the $H_0$ values obtained in the different measurements.
• Figure 3: Estimated values of the current matter energy density $\Omega_mh^2$, Hubble constant $H_0$ and sound horizon $r_dh$ in terms of various data points for different models discussed throughout Section \ref{['earlyDE']}. The cyan horizontal band corresponds to the $H_0$ value measured by R20 Riess:2020fzl, the yellow vertical band to the $\Omega_mh^2$ value estimated by Planck 2018 Aghanim:2018eyx in a $\Lambda$CDM scenario, and the light green horizontal band to the $r_d h$ value measured by BAO data. The points sharing the same symbol refer to the same model in the same paper, and the different colors indicate a different dataset combination.
• Figure 4: Whisker plot with the 68% marginalized Hubble constant constraints for the models of Section \ref{['earlyDE']}. The cyan vertical band corresponds to the $H_0$ value measured by R20 Riess:2020fzl and the light pink vertical band corresponds to the $H_0$ value estimated by Planck 2018 Aghanim:2018eyx in a $\Lambda$CDM scenario. For each line, when more than one error bar is shown, the dotted one corresponds to the Planck only constraint on the Hubble constant, while the solid one to the different dataset combinations reported in the red legend, in order to appreciate the shift due to the additional datasets.
• Figure 5: Estimated values of the current matter energy density $\Omega_mh^2$, Hubble constant $H_0$ and sound horizon $r_dh$ in terms of various data points for different models discussed throughout Section \ref{['lateDE']}. The cyan horizontal band corresponds to the $H_0$ value measured by R20 Riess:2020fzl, the yellow vertical band to the $\Omega_mh^2$ value estimated by Planck 2018 Aghanim:2018eyx in a $\Lambda$CDM scenario, and the light green horizontal band to the $r_dh$ value measured by BAO data. The points sharing the same symbol refer to the same model in the same paper, and the different colors indicate a different dataset combination.