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 4 sigma to 6 sigma 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 1-2 sigma 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 3 sigma 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.

Abstract: Interacting dark energy models may play a crucial role in explaining several important observational issues in modern cosmology and also may provide a solution to current cosmological tensions. Since the phenomenology of the dark sector could be extremely rich, one should not restrict the interacting models to have a coupling parameter which is constant in cosmic time, rather allow for its dynamical behaviour, as it is common practice in the literature when dealing with other dark energy properties, as the dark energy equation of state. We present here a compendium of the current cosmological constraints on a large variety of interacting models, investigating scenarios where the coupling parameter of the interaction function and the dark energy equation of state can be either constant or dynamical. For the most general schemes, in which both the coupling parameter of the interaction function and the dark energy equation of state are dynamical, we find 95% CL evidence for a dark energy component at early times and slightly milder evidence for a dynamical dark coupling for the most complete observational data set exploited here, which includes CMB, BAO and Supernova Ia measurements. Interestingly, there are some cases where a dark energy component different from the cosmological constant case at early times together with a coupling different from zero today, can alleviate both the H-0 and S-8 tension for the full dataset combination considered here. Due to the energy exchange among the dark sectors, the current values of the matter energy density and of the clustering parameter sigma(8) are shifted from their ACDM-like values. This fact makes future surveys, especially those focused on weak lensing measurements, unique tools to test the nature and the couplings of the dark energy sector. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Abstract: Coupled dark matter-dark energy scenarios arc modeled via a dimensionless parameter xi, which controls the strength of their interaction. While this coupling is commonly assumed to be constant, there is no underlying physical law or symmetry that forbids a time-dependent xi parameter. The most general and complete interacting scenarios between the two dark sectors should therefore allow for such a possibility, and it is the main purpose of this study to constrain two possible and well-motivated coupled cosmologies by means of the most recent and accurate early- and late-time universe observations. We find that CMB data alone prefer xi(z) > 0 and therefore a smaller amount of dark matter, alleviating some crucial and well-known cosmological data tensions. An objective assessment of the Bayesian evidence for the coupled models explored here shows no particular preference for the presence of a dynamical dark sector coupling.

Abstract: We investigate generalized interacting dark matter-dark energy scenarios with a time-dependent coupling parameter, allowing also for freedom in the neutrino sector. The models are tested in the phantom and quintessence regimes, characterized by equations of state, w(x) < -1 and w(x) > -1, respectively. Our analyses show that for some of the scenarios, the existing tensions on the Hubble constant H-0 and on the clustering parameter S-8 can be significantly alleviated. The relief is either due to (a) a dark energy component which lies within the phantom region or (b) the presence of a dynamical coupling in quintessence scenarios. The inclusion of massive neutrinos into the interaction schemes does not affect either the constraints on the cosmological parameters or the bounds on the total number or relativistic degrees of freedom N-eff, which are found to be extremely robust and, in general, strongly consistent with the canonical prediction N-eff = 3.045. The most stringent bound on the total neutrino mass M-nu is M-nu, < 0.116 eV and it is obtained within a quintessence scenario in which the matter mass-energy density is only mildly affected by the presence of a dynamical dark sector coupling.

Abstract: The Phenomenologically Emergent Dark Energy model, a dark energy model with the same number of free parameters as the flat Lambda CDM, has been proposed as a working example of a minimal model which can avoid the current cosmological tensions. A straightforward question is whether or not the inclusion of massive neutrinos and extra relativistic species may spoil such an appealing phenomenological alternative. We present the bounds on M-nu and N-eff and comment on the long standing H-0 and sigma(8) tensions within this cosmological framework with a wealth of cosmological observations. Interestingly, we find, at 95% confidence level, and with the most complete set of cosmological observations, M-nu similar to 0.21(-0.14)(+0.15) eV and N-eff = 3.03 +/- 0.32 i.e. an indication for a non-zero neutrino mass with a significance above 2 sigma. The well known Hubble constant tension is considerably easened, with a significance always below the 2 sigma level. (C) 2020 Elsevier B.V. All rights reserved.