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.

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We investigate the observational consequences of a novel class of stable interacting dark energy (IDE) models, featuring interactions between dark matter (DM) and dark energy (DE). In the first part of our work, we start by considering two IDE models which are known to present earlytime linear perturbation instabilities. Applying a transformation depending on the dark energy equation of state (EoS) to the DM-DE coupling, we then obtain two novel stable IDE models. Subsequently, we derive robust and accurate constraints on the parameters of these models, assuming a constant EoS wx for the DE fluid, in light of some of the most recent publicly available cosmological data. These include Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements from the Planck satellite, a selection of Baryon Acoustic Oscillation measurements, Supernovae Type-Ia luminosity distance measurements from the JLA sample, and measurements of the Hubble parameter up to redshift 2 from cosmic chronometers. Our analysis displays a mild preference for the DE fluid residing in the phantom region (wx < −1), with significance up to 95% confidence level, while we obtain new upper limits on the coupling parameter between the dark components. The preference for a phantom DE suggests a coupling function Q < 0, thus a scenario where energy flows from the DE to the DM. We also examine the possibility of addressing the H0 and σ8 tensions, finding that only the former can be partially alleviated. Finally, we perform a Bayesian model comparison analysis to quantify the possible preference for the two IDE models against the standard concordance ΛCDM model, finding that the latter is always preferred with the strength of the evidence ranging from positive to very strong. 98.80.Cq, 95.35.+d, 95.36.+x, 98.80.Es. *

Abstract:We use the local value of the Hubble constant recently measured with 2.4% precision, as well as the latest compilation of cosmic chronometers data, together with standard probes such as Supernovae Type Ia and Baryon Acoustic Oscillation distance measurements, in order to impose constraints on the viable and most used f (T ) gravity models, where T is the torsion scalar in teleparallel gravity. In particular, we consider three f (T ) models with two parameters, out of which one is independent, and we quantify their deviation from ΛCDM cosmology through a sole parameter. Our analysis reveals that for one of the models a small but non-zero deviation from ΛCDM cosmology is slightly favored, while for the other models the best fit is very close to ΛCDM scenario. Clearly, f (T ) gravity is consistent with observations, and it can serve as a candidate for modified gravity.