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: 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: Recent measurements of the Cosmic Microwave Anisotropies power spectra measured by the Planck satellite show a preference for a closed universe at more than 99 per cent confidence level (CL). Such a scenario is however in disagreement with several low redshift observables, including luminosity distances of Type Ia supernovae. Here we show that interacting dark energy (IDE) models can ease the discrepancies between Planck and supernovae Ia data in a closed Universe, leading to a preference for both a coupling and a curvature different from zero above the 99 per cent CL. Therefore IDE cosmologies remain as very appealing scenarios, as they can provide the solution to a number of observational tensions in different fiducial cosmologies. The results presented here strongly favour broader analyses of cosmological data, and suggest that relaxing the usual flatness and vacuum energy assumptions can lead to a much better agreement among theory and observations.