Abstract
The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. 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 4σ to 6σ disagreement between predictions of the Hubble constant, H 0, made by the early time probes in concert with the ‘vanilla’ ΛCDM cosmological 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 demands a hypothesis with enough rigor to explain multiple observations—whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1–2σ between Planck 2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess, et al (2021 Astrophys. J. 908 L6) measurement of the Hubble constant (H 0 = 73.2 ± 1.3 km s−1 Mpc−1 at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3σ disagreement level. In many cases, reduced tension comes not simply from a change in the value of H 0 but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and 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.
Highlights
The standard cosmological scenario, the so-called Λ-cold dark matter (ΛCDM) model, provides a remarkable fit to the bulk of available cosmological data, we should not forget that there is little understanding of the nature of its largest components
We classify many proposals to resolve the Hubble puzzle in different categories: we discuss the early dark energy (DE) models in section 4, the late DE proposals in section 5, the DE models with 6 degrees of freedom and their extensions in section 6, models predicting extra relativistic degrees of freedom that can be parameterized by the effective number of neutrino species Neff in section 7, models with extra interactions between the different components of the Universe in section 8, unified cosmologies in section 9, modified gravity scenarios in section 10, inflationary models in section 11, models of modified recombination history in section 12, models based on the physics of the critical phenomena in section 13, and in section 14 we present other alternative proposals
For n = 2, the Planck data and the R20 measurement are in better agreement than in the canonical ΛCDM framework, provided a modest tuning to justify the absence of lower orders in the potential [242]
Summary
The standard cosmological scenario, the so-called Λ-cold dark matter (ΛCDM) model, provides a remarkable fit to the bulk of available cosmological data, we should not forget that there is little understanding of the nature of its largest components. At this point, we classify many proposals to resolve the Hubble puzzle in different categories: we discuss the early DE models, the late DE proposals, the DE models with 6 degrees of freedom and their extensions, models predicting extra relativistic degrees of freedom that can be parameterized by the effective number of neutrino species Neff, models with extra interactions between the different components of the Universe, unified cosmologies, modified gravity scenarios, inflationary models, models of modified recombination history, models based on the physics of the critical phenomena, and in section 14 we present other alternative proposals. In figure B1 we show the combined effort made by the entire scientific community to solve or alleviate the Hubble constant tension until today. A sample code for producing the whisker plots associated with this work is made publicly available online at github.com/lucavisinelli/H0TensionRealm
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