We investigate interacting scenarios that belong to a wider class, since they include a dynamical dark energy component whose equation of state follows various one-parameter parametrizations. We confront them with the latest observational data from the cosmic microwave background, the joint light-curve sample from type Ia supernovae, baryon acoustic oscillations, Hubble parameter measurements from cosmic chronometers (CC), and a Gaussian prior on the Hubble parameter $H_0$. In all examined scenarios we find a nonzero interaction; nevertheless, the noninteracting case is allowed within $2\sigma$. Concerning the current value of the dark energy equation of state for all combinations of data sets, it always lies in the phantom regime at more than 2–3 standard deviations. Finally, for all interacting models, independently of the combination of data sets considered, the estimated values of the present Hubble parameter $H_0$ are greater compared to the $\mathrm{\Lambda }\mathrm{CDM}$-based Planck estimate and close to the local measurements, thus alleviating the $H_0$ tension.

The phenomenological parametrizations of dark-energy (DE) equations of state can be very helpful, since they allow for the investigation of its cosmological behavior despite the fact that its underlying theory is unknown. However, although there has been a large amount of research on DE parametrizations which involve two or more free parameters, the one-parameter parametrizations seem to be underestimated. We perform a detailed observational confrontation of five one-parameter DE models, with observational data from cosmic microwave background (CMB), Joint light-curve analysis sample from Supernovae Type Ia observations (JLA), baryon acoustic oscillations (BAO) distance measurements, and cosmic chronometers (CC). We find that all models favor a phantom DE equation of state at present time, while they lead to $H_0$ values in perfect agreement with its direct measurements and therefore they offer an alleviation to the $H_0$-tension. Finally, performing a Bayesian analysis we show that although $\mathrm{\Lambda }\mathrm{CDM}$ cosmology is still favored, one-parameter DE models have similar or better efficiency in fitting the data comparing to two-parameter DE parametrizations, and thus they deserve a thorough investigation.

The paper deals with a theoretical model for interacting dark energy (DE). The interaction between the cold dark matter (dust) and the DE has been assumed to be non-gravitational in nature. Exact analytic cosmological solutions are obtained both for constant and variable EoS for DE. It is found that, for very small value of the coupling parameter (in the interaction term), the model asymptotically extends up to Λ cold dark matter, while the model can enter into the phantom domain asymptotically, if the coupling parameter is not so small. Both the solutions are then analysed with 194 Supernovae Type Ia data. The best-fitting parameters are shown with 1σ and 2σ confidence intervals. Finally, we have discussed the cosmographic parameters for both the cases.

Assuming a nongravitational interaction among the dark fluids of our Universe—namely, dark matter and dark energy—we study a specific interaction model in the background of a spatially flat Friedmann-Lemaître-Robertson-Walker geometry. We find that the interaction model solves the background evolution in an analytic way when the dark energy takes a constant barotropic equation of state, $w_x$. In particular, we analyze two separate interaction scenarios, namely, when the dark energy is a fluid other than the vacuum energy (i.e., $w_x\ne -1$) and when it is vacuum energy itself (i.e., $w_x=-1$). We find that the interacting model with $w_x\ne -1$ produces stable perturbations at large scales for $w_x<-1$ with the coupling strength $\xi <0$. Both scenarios are constrained by the latest astronomical data. The analyses show that a very small interaction with the coupling strength is allowed, and within the 68.3% confidence region $\xi =0$ is recovered. The analyses further show that a large coupling strength significantly affects the large-scale dynamics of the Universe, while according to the observational data the interaction models are very well consistent with $\mathrm{\Lambda }$ cosmology. Furthermore, we observe that for the vacuum interaction scenario, the tension on $H_0$ is not released while for the interacting dark energy scenario with $w_x<-1$, the tension on $H_0$ seems to be released partially because of the high error bars in $H_0$. Finally, we conclude the work by calculating the Bayesian evidence, which shows that $\mathrm{\Lambda }\mathrm{CDM}$ cosmology is favored over the two interacting scenarios.