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

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 850 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 [2] 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.

Improved cosmological constraints on the neutrino mass and lifetime

“…In case of a neutrino mass discovery at KATRIN, a more involved analysis including inversedecays would be necessary to firmly confirm that the decay scenario can reconcile laboratory and cosmological measurements. Additionally, our results show that the tentative exclusion of the inverted mass ordering [42][43][44][45], based solely on the fact that the inverted ordering predicts m ν > 0.1 eV, is highly dependent on the hypothesis that neutrinos are stable on cosmological time-scales. Nonrelativistic decays can still easily reconcile the inverted ordering with cosmological data.…”

“…In recent years, a number of studies have attempted to constrain the neutrino mass ordering, showing that under the assumption of stable neutrinos, the inverted ordering is now disfavored by a compilation of cosmological data [42][43][44] as well as from Ly-α observations [45]. However, these arguments are centered on the fact that these analyse leads to a constraint on m ν at odds with the lower bound on the sum of neutrino masses in the case of inverted ordering, m ν 0.1 eV.…”

Using peculiar velocity surveys to constrain neutrino masses

“…Allowing 𝑁 eff to be a free parameter may be particularly interesting in the context of the Hubble tension (a potential solution to the problem involves allowing for extra species of neutrinos, i.e. 'dark radiation', (Di Valentino et al 2021), and 𝑁 eff is particularly degenerate with 𝑚 𝜈 ). Furthermore, in the case we would like an independent comparison of constraints on 𝑚 𝜈 between early Universe probes (such as the constraints from the Planck measurements of the CMB) and late Universe probes (such as galaxy surveys), we have demonstrated that peculiar velocities allow this to be possible.…”

A model-independent test of speed of light variability with cosmological observations

“…Nonetheless, this model suffers from unsolved issues -such as the fine-tuning and the primordial singularity problems, to name a few. As of recently, tensions between cosmological parameter measurements within its framework have been persisting -the most stringent at the moment being the 4.5σ tension between the H 0 measured in the late-and early-time Universe from SNe and CMB, respectively [17,18].…”