Observational constraints on sign-changeable interaction models and alleviation of the $H_0$ tension

We investigate various scenarios which include interaction forms between dark matter and dark energy that exhibit sign reverse, namely where the transfer of energy between the dark fluids changes sign during evolution. We study the large-scale inhomogeneities in such interacting scenarios and we confront them with the latest astronomical data. Our analysis shows that the sign-changeable interaction models are able to produce stable perturbations. Additionally, the data seem to slightly favor a non-zero interaction, however, within $1\sigma$ confidence level (CL) the scenarios cannot be distinguished from non-interacting cosmologies. We find that the best-fit value of the dark-energy equation-of-state parameter lies in the phantom regime, while the quintessence region is also allowed nevertheless at more than 2$\sigma$ CL. Examining the effect of the interaction on the CMB TT and matter power spectra we show that while from the simple spectra it is hard to distinguish the interacting case from $\Lambda$CDM scenario, in the residual graphs the interaction is indeed traceable. Moreover, we find that sign-changeable interaction models can reconcile the $H_0$ tension, however the $\sigma_8$ tension is still persisting. Finally, we examine the validity of the laws of thermodynamics and we show that the generalized second law is always satisfied, while the second derivative of the total entropy becomes negative at late times which implies that the universe tends towards thermodynamic equilibrium.