Modeling interacting dark energy models with Chebyshev polynomials: Exploring their constraints and effects

In this work, we examine the main cosmological effects derived from a time-varying coupling ($\bar{Q}$) between a dark matter (DM) fluid and a dark energy (DE) fluid with time-varying DE equation state (EoS) parameter ($\omega_{DE}$), in two different coupled DE models. These scenarios were built in terms of Chebyschev polynomials. Our results show that such models within dark sector can suffer an instability in their perturbations at early times and a slight departure on the amplitude of the cosmic structure growth ($f\sigma_{8}$) from the standard background evolution of the matter. These effects depend on the form of both $\bar{Q}$ and $\omega_{DE}$. Here, we also perform a combined statistical analysis using current data to put tighter constraints on the parameters space. Finally, we use some selections criteria to distinguish our models.