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.
